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All questions of Elementary Mensuration for Class 7 Exam
Three pipes A, B and C can fill an empty tank fully in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?- a)5/11
- b)6/11
- c)7/11
- d)8/11
Correct answer is option 'B'. Can you explain this answer?
Three pipes A, B and C can fill an empty tank fully in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?
a)
5/11
b)
6/11
c)
7/11
d)
8/11
|
Lakshmi Reddy answered |
Part filled by (A + B + C) in 3 minutes = 3 (1/30 + 1/20 + 1/10) = (3 × 11/60) = 11/20
Part filled by C in 3 minutes = 3/10
∴ Required ratio = (3/10 × 20/11) = 6/11
Part filled by C in 3 minutes = 3/10
∴ Required ratio = (3/10 × 20/11) = 6/11
What is the volume of a cube?
I. The area of each face of the cube is 64 square metres.
II. The length of one side of the cube is 8 metres.- a)I alone sufficient while II alone not sufficient to answer
- b)II alone sufficient while I alone not sufficient to answer
- c)Either I or II alone sufficient to answer
- d)Both I and II are not sufficient to answer
Correct answer is option 'C'. Can you explain this answer?
What is the volume of a cube?
I. The area of each face of the cube is 64 square metres.
II. The length of one side of the cube is 8 metres.
I. The area of each face of the cube is 64 square metres.
II. The length of one side of the cube is 8 metres.
a)
I alone sufficient while II alone not sufficient to answer
b)
II alone sufficient while I alone not sufficient to answer
c)
Either I or II alone sufficient to answer
d)
Both I and II are not sufficient to answer
|
Simran Deshpande answered |
Let each edge be a metre.
Then, I. a2 = 64
a = 8 m
Volume = (8 × 8 × 8) m3 = 512 m3
Thus, I alone gives the answer.
II. a = 8 m
Volume = (8 × 8 × 8) m3 = 512 m3
Thus, II alone gives the answer.
∴ Correct answer is (c).
Then, I. a2 = 64
a = 8 m
Volume = (8 × 8 × 8) m3 = 512 m3
Thus, I alone gives the answer.
II. a = 8 m
Volume = (8 × 8 × 8) m3 = 512 m3
Thus, II alone gives the answer.
∴ Correct answer is (c).
The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.- a)30 π m2
- b)40 π m2
- c)60 π m2
- d)80 π m2
Correct answer is option 'C'. Can you explain this answer?
The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.
a)
30 π m2
b)
40 π m2
c)
60 π m2
d)
80 π m2
|
Jithin Chawla answered |
l = 10 m
h = 8 m
∴ Curved surface area = πrl
= (π × 6 × 10) m2 = 60 π m2
h = 8 m
∴ Curved surface area = πrl
= (π × 6 × 10) m2 = 60 π m2
The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.- a)3 : 7
- b)7 : 3
- c)6 : 7
- d)7 : 6
Correct answer is option 'B'. Can you explain this answer?
The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.
a)
3 : 7
b)
7 : 3
c)
6 : 7
d)
7 : 6
|
Prateek Sharma answered |
(πr2h)/ (2πrh) = 924/264
r = [(924 /264) × 2] = 7 m and, 2πrh = 264
h = (264 × 7/22 × 1/2 × 1/7) = 6 m
∴ Required ratio = 2r/h =14/6 = 7 : 3
r = [(924 /264) × 2] = 7 m and, 2πrh = 264
h = (264 × 7/22 × 1/2 × 1/7) = 6 m
∴ Required ratio = 2r/h =14/6 = 7 : 3
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?- a)34
- b)40
- c)68
- d)88
Correct answer is option 'D'. Can you explain this answer?
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?
a)
34
b)
40
c)
68
d)
88
|
Keerthana Basak answered |
We have: l = 20 ft and lb = 680 sq. ft.
So, b = 34 ft.
∴ Length of fencing = (l + 2b)
= (20 + 68) ft = 88 ft.
So, b = 34 ft.
∴ Length of fencing = (l + 2b)
= (20 + 68) ft = 88 ft.
A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?- a)2 : 1
- b)3 : 2
- c)25 : 18
- d)27 : 20
Correct answer is option 'C'. Can you explain this answer?
A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?
a)
2 : 1
b)
3 : 2
c)
25 : 18
d)
27 : 20
|
Nitya Sen answered |
Volume of the large cube = (33 + 43 + 53)
= 216 cm3
Let the edge of the large cube be a.
So, a3 = 216 a = 6 cm
∴ Required ratio
= [6 × (32 + 42 + 52)]/ (6 × 62)
= 50/36 = 25 : 18
= 216 cm3
Let the edge of the large cube be a.
So, a3 = 216 a = 6 cm
∴ Required ratio
= [6 × (32 + 42 + 52)]/ (6 × 62)
= 50/36 = 25 : 18
What will be the cost of painting the inner walls of a room if the rate of painting is Rs 20 per square foot?
I. Circumference of the floor is 44 feet.
II. The height of the wall of the room is 12 feet.- a)I alone sufficient while II alone not sufficient to answer
- b)II alone sufficient while I alone not sufficient to answer
- c)Either I or II alone sufficient to answer
- d)Both I and II are necessary to answer
Correct answer is option 'D'. Can you explain this answer?
What will be the cost of painting the inner walls of a room if the rate of painting is Rs 20 per square foot?
I. Circumference of the floor is 44 feet.
II. The height of the wall of the room is 12 feet.
I. Circumference of the floor is 44 feet.
II. The height of the wall of the room is 12 feet.
a)
I alone sufficient while II alone not sufficient to answer
b)
II alone sufficient while I alone not sufficient to answer
c)
Either I or II alone sufficient to answer
d)
Both I and II are necessary to answer
|
Sanya patil answered |
Cost of Painting Inner Walls of a Room
Given: The rate of painting is Rs 20 per square foot.
To find: The cost of painting the inner walls of a room.
I. Circumference of the floor is 44 feet.
II. The height of the wall of the room is 12 feet.
Solution:
We know that the area of the wall to be painted is given by:
Area = Height x Circumference
I. From statement I, we can calculate the circumference of the floor which is needed to find the area of the wall.
Thus, statement I alone is not sufficient to calculate the cost of painting.
II. From statement II, we can find the height of the wall which is needed to find the area of the wall.
Thus, statement II alone is not sufficient to calculate the cost of painting.
Together, we can use both statements to find the area of the wall.
Area = Height x Circumference
Area = 12 x 44
Area = 528 square feet
Therefore, the cost of painting the inner walls of the room is:
Cost = Area x Rate
Cost = 528 x 20
Cost = Rs 10,560
Hence, both statements I and II are necessary to answer the question.
Given: The rate of painting is Rs 20 per square foot.
To find: The cost of painting the inner walls of a room.
I. Circumference of the floor is 44 feet.
II. The height of the wall of the room is 12 feet.
Solution:
We know that the area of the wall to be painted is given by:
Area = Height x Circumference
I. From statement I, we can calculate the circumference of the floor which is needed to find the area of the wall.
Thus, statement I alone is not sufficient to calculate the cost of painting.
II. From statement II, we can find the height of the wall which is needed to find the area of the wall.
Thus, statement II alone is not sufficient to calculate the cost of painting.
Together, we can use both statements to find the area of the wall.
Area = Height x Circumference
Area = 12 x 44
Area = 528 square feet
Therefore, the cost of painting the inner walls of the room is:
Cost = Area x Rate
Cost = 528 x 20
Cost = Rs 10,560
Hence, both statements I and II are necessary to answer the question.
A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is:- a)3.6 kg
- b)3.696 kg
- c)36 kg
- d)36.9 kg
Correct answer is option 'B'. Can you explain this answer?
A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is:
a)
3.6 kg
b)
3.696 kg
c)
36 kg
d)
36.9 kg
|
Anmol Iyer answered |
External radius = 4 cm,
Internal radius = 3 cm.
Volume of iron
= (22/7 × [(4)2 – (3)2] × 21) cm3
= (22/7 × 7 × 1 × 21) cm3
= 462 cm3
∴ Weight of iron= (462 × 8) gm
= 3696 gm
= 3.696 kg
Internal radius = 3 cm.
Volume of iron
= (22/7 × [(4)2 – (3)2] × 21) cm3
= (22/7 × 7 × 1 × 21) cm3
= 462 cm3
∴ Weight of iron= (462 × 8) gm
= 3696 gm
= 3.696 kg
A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:- a)4830
- b)5120
- c)6420
- d)8960
Correct answer is option 'B'. Can you explain this answer?
A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:
a)
4830
b)
5120
c)
6420
d)
8960
|
Rithika Roy answered |
Clearly, l = (48 – 16)m = 32 m,
b = (36 – 16)m = 20 m
h = 8 m.
∴ Volume of the box = (32 × 20 × 8) m3
= 5120 m3
b = (36 – 16)m = 20 m
h = 8 m.
∴ Volume of the box = (32 × 20 × 8) m3
= 5120 m3
If both the pipes are opened, how many hours will be taken to fill the tank?
I. The capacity of the tank is 400 litres.
II. The pipe A fills the tank in 4 hours.
III. The pipe B fills the tank in 6 hours.- a)Only I and II
- b)Only II and III
- c)All I, II and III
- d)Any two of the three
Correct answer is option 'B'. Can you explain this answer?
If both the pipes are opened, how many hours will be taken to fill the tank?
I. The capacity of the tank is 400 litres.
II. The pipe A fills the tank in 4 hours.
III. The pipe B fills the tank in 6 hours.
I. The capacity of the tank is 400 litres.
II. The pipe A fills the tank in 4 hours.
III. The pipe B fills the tank in 6 hours.
a)
Only I and II
b)
Only II and III
c)
All I, II and III
d)
Any two of the three
|
Aditi Dey answered |
II. Part of the tank filled by A in 1 hour = 1/4
III. Part of the tank filled by B in 1 hour = 1/6
(A + B)’s 1 hour’s work = (1/4 + 1/6) = 5/12
∴ A and B will fill the tank in 12/5hrs
= 2 hrs 24 min.
So, II and III are needed.
∴ Correct answer is (b).
III. Part of the tank filled by B in 1 hour = 1/6
(A + B)’s 1 hour’s work = (1/4 + 1/6) = 5/12
∴ A and B will fill the tank in 12/5hrs
= 2 hrs 24 min.
So, II and III are needed.
∴ Correct answer is (b).
What is the volume of 32 metre high cylindrical tank?
I. The area of its base is 154 m2.
II. The diameter of the base is 14 m.- a)I alone sufficient while II alone not sufficient to answer
- b)II alone sufficient while I alone not sufficient to answer
- c)Either I or II alone sufficient to answer
- d)Both I and II are not sufficient to answer
Correct answer is option 'C'. Can you explain this answer?
What is the volume of 32 metre high cylindrical tank?
I. The area of its base is 154 m2.
II. The diameter of the base is 14 m.
I. The area of its base is 154 m2.
II. The diameter of the base is 14 m.
a)
I alone sufficient while II alone not sufficient to answer
b)
II alone sufficient while I alone not sufficient to answer
c)
Either I or II alone sufficient to answer
d)
Both I and II are not sufficient to answer
|
|
Anmol Iyer answered |
Given, height = 32 m
From I, the area of the base = 154 m2
∴ Volume = (Area of the base × Height)
= (154 × 32) m3
Thus, I alone gives the answer.
From II, the radius of the base = 7 m
∴ Volume = π r2h = (22/7 × 7 × 7 × 32) m3
= 4928 m3
Thus, II alone gives the answer.
∴ Correct answer is (c).
From I, the area of the base = 154 m2
∴ Volume = (Area of the base × Height)
= (154 × 32) m3
Thus, I alone gives the answer.
From II, the radius of the base = 7 m
∴ Volume = π r2h = (22/7 × 7 × 7 × 32) m3
= 4928 m3
Thus, II alone gives the answer.
∴ Correct answer is (c).
The percentage increase in the area of a rectangle, if each of its sides is increased by 20%, is:- a)40%
- b)42%
- c)44%
- d)46%
Correct answer is option 'C'. Can you explain this answer?
The percentage increase in the area of a rectangle, if each of its sides is increased by 20%, is:
a)
40%
b)
42%
c)
44%
d)
46%
|
Anand Choudhury answered |
Let original length = x metres and original breadth = y metres.
Original area = (xy) m2.
New length = (120/100) × m = (6/5) × m
New breadth = (120/100) y m = (6/5) y m
New area = (6/5) × m × (6/5) y m
= (36/25)xy m2
The difference between the original area
= xy and new area 36/25 xy is
= (36/25)xy – xy
= xy( 36/25 – 1)
= xy( 11/25) or (11/25)xy
∴ Increase %
= [(11/25)xy × 1/xy × 100]%
= 44%
Original area = (xy) m2.
New length = (120/100) × m = (6/5) × m
New breadth = (120/100) y m = (6/5) y m
New area = (6/5) × m × (6/5) y m
= (36/25)xy m2
The difference between the original area
= xy and new area 36/25 xy is
= (36/25)xy – xy
= xy( 36/25 – 1)
= xy( 11/25) or (11/25)xy
∴ Increase %
= [(11/25)xy × 1/xy × 100]%
= 44%
A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:- a)90 cm
- b)1 dm
- c)1 m
- d)1.1 cm
Correct answer is option 'B'. Can you explain this answer?
A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:
a)
90 cm
b)
1 dm
c)
1 m
d)
1.1 cm
|
Pranjal Banerjee answered |
Let the thickness of the bottom be x cm.
Then, [(330 – 10) × (260 – 10) × (110 × x)]
= 8000 × 1000
⇒ 320 × 250 × (110 – x) = 8000 × 1000
⇒ (110 – x) = (8000 × 1000)/ (320 × 250) = 100
x = 10 cm = 1 dm
Then, [(330 – 10) × (260 – 10) × (110 × x)]
= 8000 × 1000
⇒ 320 × 250 × (110 – x) = 8000 × 1000
⇒ (110 – x) = (8000 × 1000)/ (320 × 250) = 100
x = 10 cm = 1 dm
A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?- a)2.91 m
- b)3 m
- c)5.82 m
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
a)
2.91 m
b)
3 m
c)
5.82 m
d)
None of these
|
Gauri Basak answered |
Area of the park = (60 × 40) m2
= 2400 m2
Area of the lawn = 2109 m2.
∴ Area of the crossroads
= (2400 – 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x – x2 = 291
⇒ x2 – 100x + 291 = 0
⇒ (x – 97)(x – 3) = 0
⇒ x = 3
= 2400 m2
Area of the lawn = 2109 m2.
∴ Area of the crossroads
= (2400 – 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x – x2 = 291
⇒ x2 – 100x + 291 = 0
⇒ (x – 97)(x – 3) = 0
⇒ x = 3
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:- a)15360
- b)153600
- c)30720
- d)307200
Correct answer is option 'B'. Can you explain this answer?
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:
a)
15360
b)
153600
c)
30720
d)
307200
|
Arindam Kumar answered |
Perimeter = Distance covered in 8 min.
= (12000/60 × 8) = 1600 m
Let length = 3x metres and breadth
= 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
∴ Length = 480 m and Breadth = 320 m.
∴ Area = (480 × 320) m2 = 153600 m2.
= (12000/60 × 8) = 1600 m
Let length = 3x metres and breadth
= 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
∴ Length = 480 m and Breadth = 320 m.
∴ Area = (480 × 320) m2 = 153600 m2.
The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?- a)25% increase
- b)50% increase
- c)50% decrease
- d)75% decrease
Correct answer is option 'B'. Can you explain this answer?
The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?
a)
25% increase
b)
50% increase
c)
50% decrease
d)
75% decrease
|
|
Gauri Basak answered |
Let original length = x
and original breadth = y
Original area = xy.
New length = x/2
New breadth = 3y.
New area = (x/2 × 3y) = (3/2)xy
∴ Increase % = (1/2)xy × (1/xy) × 100%
= 50%
and original breadth = y
Original area = xy.
New length = x/2
New breadth = 3y.
New area = (x/2 × 3y) = (3/2)xy
∴ Increase % = (1/2)xy × (1/xy) × 100%
= 50%
Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:- a)60 gallons
- b)100 gallons
- c)120 gallons
- d)180 gallons
Correct answer is option 'C'. Can you explain this answer?
Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:
a)
60 gallons
b)
100 gallons
c)
120 gallons
d)
180 gallons
|
Pallavi Banerjee answered |
Work done by the waste pipe in 1 minute
=1/15 – (1/20 + 1/24)
= (1/15 – 11/20)
= – 1/40 [–ve sign means emptying]
∴ Volume of 1/40 part = 3 gallons
Volume of whole = (3 × 40) gallons
= 120 gallons
=1/15 – (1/20 + 1/24)
= (1/15 – 11/20)
= – 1/40 [–ve sign means emptying]
∴ Volume of 1/40 part = 3 gallons
Volume of whole = (3 × 40) gallons
= 120 gallons
How long will it take to empty the tank if both the inlet pipe A and the outlet pipe B are opened simultaneously?
I. A can fill the tank in 16 minutes.
II. B can empty the full tank in 8 minutes.- a)I alone sufficient while II alone not sufficient to answer
- b)II alone sufficient while I alone not sufficient to answer
- c)Either I or II alone sufficient to answer
- d)Both I and II are necessary to answer
Correct answer is option 'D'. Can you explain this answer?
How long will it take to empty the tank if both the inlet pipe A and the outlet pipe B are opened simultaneously?
I. A can fill the tank in 16 minutes.
II. B can empty the full tank in 8 minutes.
I. A can fill the tank in 16 minutes.
II. B can empty the full tank in 8 minutes.
a)
I alone sufficient while II alone not sufficient to answer
b)
II alone sufficient while I alone not sufficient to answer
c)
Either I or II alone sufficient to answer
d)
Both I and II are necessary to answer
|
|
Lakshmi Reddy answered |
I. A’s 1 minute’s filling work = 1/16
II. B’s 1 minute’s filling work =1/8
(A + B)’s 1 minute’s emptying work
= (1/8 – 1/16) =1/16
∴ Tank will be emptied in 16 minutes.
Thus, both I and II are necessary to answer the question.
∴ Correct answer is (d).
II. B’s 1 minute’s filling work =1/8
(A + B)’s 1 minute’s emptying work
= (1/8 – 1/16) =1/16
∴ Tank will be emptied in 16 minutes.
Thus, both I and II are necessary to answer the question.
∴ Correct answer is (d).
A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:- a)12π cm3
- b)15π cm3
- c)16π cm3
- d)20π cm3
Correct answer is option 'A'. Can you explain this answer?
A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:
a)
12π cm3
b)
15π cm3
c)
16π cm3
d)
20π cm3
|
|
Jithin Chawla answered |
Clearly, we have r = 3 cm and h = 4 cm.
∴ Volume = 1/3 πr2h
= (1/3 × π × 32 × 4) cm3
= 12π cm3
The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?- a)16 cm
- b)18 cm
- c)24 cm
- d)Data inadequate
Correct answer is option 'B'. Can you explain this answer?
The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
a)
16 cm
b)
18 cm
c)
24 cm
d)
Data inadequate
|
Bhaskar Patel answered |
To solve this problem, we need to use the given information about the ratio between the perimeter and breadth of the rectangle, as well as the area of the rectangle.
Let's assume the length of the rectangle is L cm and the breadth is B cm.
Given:
Ratio of perimeter to breadth = 5:1
Perimeter = 2(L + B)
Area = L * B = 216 sq. cm
To find the length of the rectangle, we can use the following steps:
Step 1: Express the ratio of perimeter to breadth in terms of L and B
Perimeter : Breadth = 5 : 1
2(L + B) : B = 5 : 1
Step 2: Solve the ratio equation
2(L + B)/B = 5/1
2L + 2B = 5B
2L = 3B
L = (3/2)B
Step 3: Substitute the value of L in terms of B into the area equation
L * B = 216
(3/2)B * B = 216
(3/2)B^2 = 216
B^2 = (2/3) * 216
B^2 = 144
B = √144
B = 12
Step 4: Find the length of the rectangle using the value of B
L = (3/2)B
L = (3/2) * 12
L = 18 cm
Therefore, the length of the rectangle is 18 cm. Hence, option B is the correct answer.
Let's assume the length of the rectangle is L cm and the breadth is B cm.
Given:
Ratio of perimeter to breadth = 5:1
Perimeter = 2(L + B)
Area = L * B = 216 sq. cm
To find the length of the rectangle, we can use the following steps:
Step 1: Express the ratio of perimeter to breadth in terms of L and B
Perimeter : Breadth = 5 : 1
2(L + B) : B = 5 : 1
Step 2: Solve the ratio equation
2(L + B)/B = 5/1
2L + 2B = 5B
2L = 3B
L = (3/2)B
Step 3: Substitute the value of L in terms of B into the area equation
L * B = 216
(3/2)B * B = 216
(3/2)B^2 = 216
B^2 = (2/3) * 216
B^2 = 144
B = √144
B = 12
Step 4: Find the length of the rectangle using the value of B
L = (3/2)B
L = (3/2) * 12
L = 18 cm
Therefore, the length of the rectangle is 18 cm. Hence, option B is the correct answer.
Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?- a)12 min
- b)15 min
- c)25 min
- d)50 min
Correct answer is option 'A'. Can you explain this answer?
Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
a)
12 min
b)
15 min
c)
25 min
d)
50 min
|
Alpana reddy answered |
Understanding the Problem
To determine how long it takes for two pipes to fill a tank when used together, we first need to find out their individual rates of filling.
Filling Rates of the Pipes
- Pipe A can fill the tank in 20 minutes.
- Rate of Pipe A = 1 tank / 20 minutes = 1/20 tanks per minute.
- Pipe B can fill the tank in 30 minutes.
- Rate of Pipe B = 1 tank / 30 minutes = 1/30 tanks per minute.
Combining the Rates
To find the combined rate of both pipes working together, we add their individual rates:
- Combined Rate = Rate of Pipe A + Rate of Pipe B
- Combined Rate = (1/20 + 1/30).
Finding a Common Denominator
To add these fractions, we need a common denominator, which is 60:
- (1/20) = 3/60
- (1/30) = 2/60
Now, we can add:
- Combined Rate = (3/60 + 2/60) = 5/60 tanks per minute.
Calculating the Time to Fill the Tank
To find out how long it takes to fill 1 tank at the combined rate:
- Time = 1 tank / (5/60) = 60/5 = 12 minutes.
Conclusion
When both pipes A and B are used together, they can fill the tank in 12 minutes, making the correct answer option 'A'.
To determine how long it takes for two pipes to fill a tank when used together, we first need to find out their individual rates of filling.
Filling Rates of the Pipes
- Pipe A can fill the tank in 20 minutes.
- Rate of Pipe A = 1 tank / 20 minutes = 1/20 tanks per minute.
- Pipe B can fill the tank in 30 minutes.
- Rate of Pipe B = 1 tank / 30 minutes = 1/30 tanks per minute.
Combining the Rates
To find the combined rate of both pipes working together, we add their individual rates:
- Combined Rate = Rate of Pipe A + Rate of Pipe B
- Combined Rate = (1/20 + 1/30).
Finding a Common Denominator
To add these fractions, we need a common denominator, which is 60:
- (1/20) = 3/60
- (1/30) = 2/60
Now, we can add:
- Combined Rate = (3/60 + 2/60) = 5/60 tanks per minute.
Calculating the Time to Fill the Tank
To find out how long it takes to fill 1 tank at the combined rate:
- Time = 1 tank / (5/60) = 60/5 = 12 minutes.
Conclusion
When both pipes A and B are used together, they can fill the tank in 12 minutes, making the correct answer option 'A'.
A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is:- a)10%
- b)10.08%
- c)20%
- d)28%
Correct answer is option 'D'. Can you explain this answer?
A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is:
a)
10%
b)
10.08%
c)
20%
d)
28%
|
Mehul Sen answered |
Let original length = x
and original breadth = y
Decrease in area
= xy – [(80/100)x × (90/100)y]
= (7/25)xy
∴ Decrease % = [(7/25)xy × 1/xy × 100]%
= 28%
and original breadth = y
Decrease in area
= xy – [(80/100)x × (90/100)y]
= (7/25)xy
∴ Decrease % = [(7/25)xy × 1/xy × 100]%
= 28%
A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:- a)12 kg
- b)60 kg
- c)72 kg
- d)96 kg
Correct answer is option 'B'. Can you explain this answer?
A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
a)
12 kg
b)
60 kg
c)
72 kg
d)
96 kg
|
|
Kalyan Unni answered |
Given data:
Length of the boat (L) = 3 m
Breadth of the boat (B) = 2 m
Sinking depth (D) = 1 cm = 0.01 m
Assumptions:
1. The boat is perfectly floating on water before the man gets on it.
2. The boat is made of a uniform material with a uniform thickness.
3. The weight of the boat is negligible compared to the weight of the man.
Principle:
When a body floats on a liquid, it displaces a volume of liquid equal to its own weight. This principle is known as Archimedes' principle.
Explanation:
Step 1: Calculate the volume of water displaced by the boat before the man gets on it.
The volume of water displaced by the boat is equal to the product of its length, breadth, and sinking depth.
Volume of water displaced by the boat = L * B * D = 3 m * 2 m * 0.01 m = 0.06 m^3
Step 2: Calculate the weight of water displaced by the boat.
The weight of water displaced by the boat is equal to the product of the volume of water displaced and the density of water.
Density of water = 1000 kg/m^3 (approximate value)
Weight of water displaced by the boat = Volume of water displaced * Density of water
Weight of water displaced by the boat = 0.06 m^3 * 1000 kg/m^3 = 60 kg
Step 3: Calculate the mass of the man.
According to Archimedes' principle, the weight of water displaced by the boat is equal to the weight of the boat and the man combined when they are floating.
Weight of the boat + Weight of the man = Weight of water displaced by the boat
Let the mass of the man be 'M' kg.
Weight of the boat = Volume of the boat * Density of water
Weight of the boat = L * B * Thickness of the boat * Density of water
Weight of the boat = 3 m * 2 m * Thickness of the boat * 1000 kg/m^3
Weight of the boat + Weight of the man = (3 m * 2 m * Thickness of the boat * 1000 kg/m^3) + M kg
Since the boat sinks by 1 cm when the man gets on it, the volume of the boat occupied by the man is equal to the product of the length, breadth, and sinking depth.
Volume of the boat occupied by the man = L * B * D = 3 m * 2 m * 0.01 m = 0.06 m^3
Using the principle of Archimedes, we can equate the weight of water displaced by the boat to the sum of the weight of the boat and the weight of the man.
(3 m * 2 m * Thickness of the boat * 1000 kg/m^3) + M kg = 0.06 m^3 * 1000 kg/m^3
Simplifying the equation, we get:
M = 60 kg
Therefore, the mass of the man is 60 kg, which corresponds to option 'B'.
Length of the boat (L) = 3 m
Breadth of the boat (B) = 2 m
Sinking depth (D) = 1 cm = 0.01 m
Assumptions:
1. The boat is perfectly floating on water before the man gets on it.
2. The boat is made of a uniform material with a uniform thickness.
3. The weight of the boat is negligible compared to the weight of the man.
Principle:
When a body floats on a liquid, it displaces a volume of liquid equal to its own weight. This principle is known as Archimedes' principle.
Explanation:
Step 1: Calculate the volume of water displaced by the boat before the man gets on it.
The volume of water displaced by the boat is equal to the product of its length, breadth, and sinking depth.
Volume of water displaced by the boat = L * B * D = 3 m * 2 m * 0.01 m = 0.06 m^3
Step 2: Calculate the weight of water displaced by the boat.
The weight of water displaced by the boat is equal to the product of the volume of water displaced and the density of water.
Density of water = 1000 kg/m^3 (approximate value)
Weight of water displaced by the boat = Volume of water displaced * Density of water
Weight of water displaced by the boat = 0.06 m^3 * 1000 kg/m^3 = 60 kg
Step 3: Calculate the mass of the man.
According to Archimedes' principle, the weight of water displaced by the boat is equal to the weight of the boat and the man combined when they are floating.
Weight of the boat + Weight of the man = Weight of water displaced by the boat
Let the mass of the man be 'M' kg.
Weight of the boat = Volume of the boat * Density of water
Weight of the boat = L * B * Thickness of the boat * Density of water
Weight of the boat = 3 m * 2 m * Thickness of the boat * 1000 kg/m^3
Weight of the boat + Weight of the man = (3 m * 2 m * Thickness of the boat * 1000 kg/m^3) + M kg
Since the boat sinks by 1 cm when the man gets on it, the volume of the boat occupied by the man is equal to the product of the length, breadth, and sinking depth.
Volume of the boat occupied by the man = L * B * D = 3 m * 2 m * 0.01 m = 0.06 m^3
Using the principle of Archimedes, we can equate the weight of water displaced by the boat to the sum of the weight of the boat and the weight of the man.
(3 m * 2 m * Thickness of the boat * 1000 kg/m^3) + M kg = 0.06 m^3 * 1000 kg/m^3
Simplifying the equation, we get:
M = 60 kg
Therefore, the mass of the man is 60 kg, which corresponds to option 'B'.
50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:- a)20 cm
- b)25 cm
- c)35 cm
- d)50 cm
Correct answer is option 'B'. Can you explain this answer?
50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:
a)
20 cm
b)
25 cm
c)
35 cm
d)
50 cm
|
|
Nitya Sen answered |
Total volume of water displaced
= (4 × 50) m3 = 200 m3
∴ Rise in water level = [200/( 40 × 20)] m
= 0.25 m =25 cm
= (4 × 50) m3 = 200 m3
∴ Rise in water level = [200/( 40 × 20)] m
= 0.25 m =25 cm
Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in:- a)6 hours
- b)6.5 hours
- c)7 hours
- d)7.5 hours
Correct answer is option 'C'. Can you explain this answer?
Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in:
a)
6 hours
b)
6.5 hours
c)
7 hours
d)
7.5 hours
|
Shalini Menon answered |
(A + B)’s 1 hour’s work = (1/12 + 1/15)
= 3/20
(A + C)’s hour’s work = (1/12 + 1/20)
= 2/15
Part filled in 2 hrs = (3/20 + 2/15) = 17/60
Part filled in 6 hrs = (3 × 17/60) = 17/20
Remaining part = (1 – 17/20) = 3/20
Now, it is the turn of A and B and 3/20 part is filled by A and B in 1 hour.
∴ Total time taken to fill the tank
= (6 + 1) hrs = 7 hrs.
= 3/20
(A + C)’s hour’s work = (1/12 + 1/20)
= 2/15
Part filled in 2 hrs = (3/20 + 2/15) = 17/60
Part filled in 6 hrs = (3 × 17/60) = 17/20
Remaining part = (1 – 17/20) = 3/20
Now, it is the turn of A and B and 3/20 part is filled by A and B in 1 hour.
∴ Total time taken to fill the tank
= (6 + 1) hrs = 7 hrs.
The area of playground is 1600 m2. What is the perimeter?
I. It is a perfect square playground.
II. It costs Rs 3200 to put a fence around the playground at the rate of Rs 20 per metre.- a)I alone sufficient while II alone not sufficient to answer
- b)II alone sufficient while I alone not sufficient to answer
- c)Either I or II alone sufficient to answer
- d)Both I and II are not sufficient to answer
Correct answer is option 'C'. Can you explain this answer?
The area of playground is 1600 m2. What is the perimeter?
I. It is a perfect square playground.
II. It costs Rs 3200 to put a fence around the playground at the rate of Rs 20 per metre.
I. It is a perfect square playground.
II. It costs Rs 3200 to put a fence around the playground at the rate of Rs 20 per metre.
a)
I alone sufficient while II alone not sufficient to answer
b)
II alone sufficient while I alone not sufficient to answer
c)
Either I or II alone sufficient to answer
d)
Both I and II are not sufficient to answer
|
|
Gauri Basak answered |
Area = 1600 m2.
I. Side = 1600 m = 40 m. So, perimeter
= (40 × 4) m = 160 m.
∴ I alone gives the answer.
II. Perimeter = Total cost = 3200 m
= 160 m
Cost per metre = 20
∴ II alone gives the answer.
∴ Correct answer is (c).
I. Side = 1600 m = 40 m. So, perimeter
= (40 × 4) m = 160 m.
∴ I alone gives the answer.
II. Perimeter = Total cost = 3200 m
= 160 m
Cost per metre = 20
∴ II alone gives the answer.
∴ Correct answer is (c).
A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:- a)Rs 456
- b)Rs 458
- c)Rs 558
- d)Rs 568
Correct answer is option 'C'. Can you explain this answer?
A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:
a)
Rs 456
b)
Rs 458
c)
Rs 558
d)
Rs 568
|
Akshara Bajaj answered |
Area to be plastered
= [2(l + b) × h] + (l × b)
= {[2(25 + 12) × 6] + (25 × 12)} m2
= (444 + 300) m2
= 744 m2.
∴ Cost of plastering = Rs (744 x 75/100)
= Rs 558
= [2(l + b) × h] + (l × b)
= {[2(25 + 12) × 6] + (25 × 12)} m2
= (444 + 300) m2
= 744 m2.
∴ Cost of plastering = Rs (744 x 75/100)
= Rs 558
What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?- a)814
- b)820
- c)840
- d)844
Correct answer is option 'A'. Can you explain this answer?
What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?
a)
814
b)
820
c)
840
d)
844
|
|
Ritika Singh answered |
Length of largest tile
= H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 × 41) cm2.
∴ Required number of tiles
= (1517 × 902)/(41 × 41) = 814
= H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 × 41) cm2.
∴ Required number of tiles
= (1517 × 902)/(41 × 41) = 814
A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:- a)720 m3
- b)900 m3
- c)1200 m3
- d)1800 m3
Correct answer is option 'C'. Can you explain this answer?
A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
a)
720 m3
b)
900 m3
c)
1200 m3
d)
1800 m3
|
Muskaan mehta answered |
Given Information:
The hall is 15 m long and 12 m broad.
Calculation:
- Let the height of the hall be h meters.
- The sum of the areas of the floor and the ceiling = 2*(15*12) = 360 m².
- The sum of the areas of the four walls = 2*(15+12)*h = 54h m².
Equation:
- 360 = 54h
- h = 360/54
- h = 6.67 meters
Volume of the Hall:
- Volume = length * breadth * height
- Volume = 15 * 12 * 6.67
- Volume = 1200 m³
Therefore, the volume of the hall is 1200 m³, which corresponds to option 'C'.
The hall is 15 m long and 12 m broad.
Calculation:
- Let the height of the hall be h meters.
- The sum of the areas of the floor and the ceiling = 2*(15*12) = 360 m².
- The sum of the areas of the four walls = 2*(15+12)*h = 54h m².
Equation:
- 360 = 54h
- h = 360/54
- h = 6.67 meters
Volume of the Hall:
- Volume = length * breadth * height
- Volume = 15 * 12 * 6.67
- Volume = 1200 m³
Therefore, the volume of the hall is 1200 m³, which corresponds to option 'C'.
Two pipes A and B can fill a cistern in 37.5 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if B is turned off after:- a)5 min
- b)9 min
- c)10 min
- d)15 min
Correct answer is option 'B'. Can you explain this answer?
Two pipes A and B can fill a cistern in 37.5 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if B is turned off after:
a)
5 min
b)
9 min
c)
10 min
d)
15 min
|
|
Shalini Menon answered |
Let B be turned off after x minutes. Then,
Part filled by (A + B) in x min. + Part filled by
A in (30 – x) min. = 1.
∴ x( 2/75 + 1/45) + (30 – x)2/75 = 1
⇒ 11x/225 + (60 – 2x)/75 = 1
⇒ 11x + 180 – 6x = 225
⇒ x = 9
Part filled by (A + B) in x min. + Part filled by
A in (30 – x) min. = 1.
∴ x( 2/75 + 1/45) + (30 – x)2/75 = 1
⇒ 11x/225 + (60 – 2x)/75 = 1
⇒ 11x + 180 – 6x = 225
⇒ x = 9
The area of a rectangle is equal to the area of right-angles triangle. What is the length of the rectangle?
I. The base of the triangle is 40 cm.
II. The height of the triangle is 50 cm.- a)I alone sufficient while II alone not sufficient to answer
- b)II alone sufficient while I alone not sufficient to answer
- c)Either I or II alone sufficient to answer
- d)Both I and II are not sufficient to answer
Correct answer is option 'D'. Can you explain this answer?
The area of a rectangle is equal to the area of right-angles triangle. What is the length of the rectangle?
I. The base of the triangle is 40 cm.
II. The height of the triangle is 50 cm.
I. The base of the triangle is 40 cm.
II. The height of the triangle is 50 cm.
a)
I alone sufficient while II alone not sufficient to answer
b)
II alone sufficient while I alone not sufficient to answer
c)
Either I or II alone sufficient to answer
d)
Both I and II are not sufficient to answer
|
Mainak Basu answered |
Given: Area of rectangle
= Area of a right-angle triangle.
⇒ l x b = ½ x B x H
I gives, B = 40 cm.
II gives, H = 50 cm.
Thus, to find l, we need b also, which is not given.
∴ Given data is not sufficient to give the answer.
∴ Correct answer is (d).
= Area of a right-angle triangle.
⇒ l x b = ½ x B x H
I gives, B = 40 cm.
II gives, H = 50 cm.
Thus, to find l, we need b also, which is not given.
∴ Given data is not sufficient to give the answer.
∴ Correct answer is (d).
What is the height of the triangle?
I. The area of the triangle is 20 times its base.
II. The perimeter of the triangle is equal to the perimeter of a square of side 10 cm.- a)I alone sufficient while II alone not sufficient to answer
- b)II alone sufficient while I alone not sufficient to answer
- c)Either I or II alone sufficient to answer
- d)Both I and II are not sufficient to answer
Correct answer is option 'A'. Can you explain this answer?
What is the height of the triangle?
I. The area of the triangle is 20 times its base.
II. The perimeter of the triangle is equal to the perimeter of a square of side 10 cm.
I. The area of the triangle is 20 times its base.
II. The perimeter of the triangle is equal to the perimeter of a square of side 10 cm.
a)
I alone sufficient while II alone not sufficient to answer
b)
II alone sufficient while I alone not sufficient to answer
c)
Either I or II alone sufficient to answer
d)
Both I and II are not sufficient to answer
|
Snehal Basak answered |
I. A = 20 x B ½ x B x H = 20 x B
⇒ H = 40.
∴ I alone gives the answer.
II gives the perimeter of the triangle = 40 cm.
This does not give the height of the triangle.
∴ Correct answer is (a).
⇒ H = 40.
∴ I alone gives the answer.
II gives the perimeter of the triangle = 40 cm.
This does not give the height of the triangle.
∴ Correct answer is (a).
An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:- a)2%
- b)2.02%
- c)4%
- d)4.04%
Correct answer is option 'D'. Can you explain this answer?
An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
a)
2%
b)
2.02%
c)
4%
d)
4.04%
|
Siddharth Sharma answered |
100 cm is read as 102 cm.
∴ A1 = (100 × 100) cm2 and
A2 = (102 × 102) cm2.
(A2 – A1) = [(102)2 – (100)2]
= (102 + 100) × (102 – 100)
= 404 cm2
∴ Percentage error
= [404/(100 × 100) × 100]% = 4.04%
∴ A1 = (100 × 100) cm2 and
A2 = (102 × 102) cm2.
(A2 – A1) = [(102)2 – (100)2]
= (102 + 100) × (102 – 100)
= 404 cm2
∴ Percentage error
= [404/(100 × 100) × 100]% = 4.04%
What is the area of the hall?
I. Material cost of flooring per square metre is Rs 2.50.
II. Labour cost of flooring the hall is Rs 3500.
III. Total cost of flooring the hall is Rs 14,500.- a)I and II only
- b)II and III only
- c)All I, II and III
- d)Any two of the three
Correct answer is option 'C'. Can you explain this answer?
What is the area of the hall?
I. Material cost of flooring per square metre is Rs 2.50.
II. Labour cost of flooring the hall is Rs 3500.
III. Total cost of flooring the hall is Rs 14,500.
I. Material cost of flooring per square metre is Rs 2.50.
II. Labour cost of flooring the hall is Rs 3500.
III. Total cost of flooring the hall is Rs 14,500.
a)
I and II only
b)
II and III only
c)
All I, II and III
d)
Any two of the three
|
|
Ritika Singh answered |
I. Material cost = Rs 2.50 per m2
II. Labour cost = Rs 3500
III. Total cost = Rs 14,500
Let the area be A sq. metres.
∴ Material cost = Rs (14500 – 3500)
= Rs 11,000
∴ 5A/2 = 11000
A = (11000 × 2)/5 = 4400 m2
Thus, all I, II and III are needed to get the answer.
∴ Correct answer is (c).
II. Labour cost = Rs 3500
III. Total cost = Rs 14,500
Let the area be A sq. metres.
∴ Material cost = Rs (14500 – 3500)
= Rs 11,000
∴ 5A/2 = 11000
A = (11000 × 2)/5 = 4400 m2
Thus, all I, II and III are needed to get the answer.
∴ Correct answer is (c).
A man walked diagonally across a square plot. Approximately, what is the percent saved by not walking along the edges?- a)20
- b)24
- c)30
- d)33
Correct answer is option 'C'. Can you explain this answer?
A man walked diagonally across a square plot. Approximately, what is the percent saved by not walking along the edges?
a)
20
b)
24
c)
30
d)
33
|
Tanishq Kulkarni answered |
Let the side of the square (ABCD) be x metres.
Then, AB + BC = 2x metres.
AC = √2x = (1.41x) m.
Saving on 2x metres = (0.59x) m.
Saving % = (0.59x/2x) × 100%
= 30 %( approx)
Then, AB + BC = 2x metres.
AC = √2x = (1.41x) m.
Saving on 2x metres = (0.59x) m.
Saving % = (0.59x/2x) × 100%
= 30 %( approx)
How much time will the leak take to empty the full cistern?
I. The cistern is normally filled in 9 hours.
II. It takes one hour more than the usual time to fill the cistern because of a leak in the bottom.- a)I alone sufficient while II alone not sufficient to answer
- b)II alone sufficient while I alone not sufficient to answer
- c)Either I or II alone sufficient to answer
- d)Both I and II are necessary to answer
Correct answer is option 'D'. Can you explain this answer?
How much time will the leak take to empty the full cistern?
I. The cistern is normally filled in 9 hours.
II. It takes one hour more than the usual time to fill the cistern because of a leak in the bottom.
I. The cistern is normally filled in 9 hours.
II. It takes one hour more than the usual time to fill the cistern because of a leak in the bottom.
a)
I alone sufficient while II alone not sufficient to answer
b)
II alone sufficient while I alone not sufficient to answer
c)
Either I or II alone sufficient to answer
d)
Both I and II are necessary to answer
|
Rhea Khanna answered |
I. Time taken to fill the cistern without leak = 9 hours.
Part of cistern filled without leak in 1 hour = 1/9
II. Time taken to fill the cistern in presence of leak = 10 hours.
Net filling in 1 hour =1/10
Work done by leak in 1 hour = (1/9 – 1/10) =1/90
∴ Leak will empty the full cistern in 90 hours.
Clearly, both I and II are necessary to answer the question.
∴ Correct answer is (d).
Part of cistern filled without leak in 1 hour = 1/9
II. Time taken to fill the cistern in presence of leak = 10 hours.
Net filling in 1 hour =1/10
Work done by leak in 1 hour = (1/9 – 1/10) =1/90
∴ Leak will empty the full cistern in 90 hours.
Clearly, both I and II are necessary to answer the question.
∴ Correct answer is (d).
Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?- a)10 min. 20 sec.
- b)11 min. 45 sec.
- c)12 min. 30 sec.
- d)14 min. 40 sec.
Correct answer is option 'D'. Can you explain this answer?
Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?
a)
10 min. 20 sec.
b)
11 min. 45 sec.
c)
12 min. 30 sec.
d)
14 min. 40 sec.
|
|
Akash Kumar answered |
To find the total time required to fill the tank, we need to calculate the rate at which the tank is being filled when both pipes A and B are open, and then use that rate to determine the time it takes to fill the remaining portion of the tank after pipe A is turned off.
Let's first calculate the rate at which each pipe fills the tank:
Pipe A fills the tank in 15 minutes, so its filling rate is 1/15 of the tank per minute.
Pipe B fills the tank in 20 minutes, so its filling rate is 1/20 of the tank per minute.
When both pipes A and B are open, their combined filling rate is the sum of their individual rates:
Combined filling rate = 1/15 + 1/20 = 4/60 + 3/60 = 7/60 of the tank per minute.
Now, let's determine the amount of water that has been filled in the tank after 4 minutes when pipe A is turned off:
In 4 minutes, both pipes A and B have been open, so the amount of water filled by both pipes is:
Amount filled in 4 minutes = (7/60) * 4 = 28/60 of the tank.
After 4 minutes, pipe A is turned off and only pipe B continues to fill the tank. We need to calculate how long it takes for pipe B to fill the remaining portion of the tank, which is 1 - 28/60 = 32/60 of the tank.
Since pipe B fills the tank at a rate of 1/20 of the tank per minute, the time it takes to fill the remaining portion of the tank is:
Time = (32/60)/(1/20) = (32/60) * (20/1) = 32/3 minutes.
Finally, to find the total time required to fill the tank, we add the time it took for both pipes to fill the tank initially (4 minutes) and the time it took for pipe B to fill the remaining portion (32/3 minutes):
Total time = 4 + 32/3 = 12 + 32/3 = 36/3 + 32/3 = 68/3 minutes.
Converting this to minutes and seconds:
Total time = 22 minutes and 40 seconds.
Therefore, the correct answer is option D) 14 minutes and 40 seconds.
Let's first calculate the rate at which each pipe fills the tank:
Pipe A fills the tank in 15 minutes, so its filling rate is 1/15 of the tank per minute.
Pipe B fills the tank in 20 minutes, so its filling rate is 1/20 of the tank per minute.
When both pipes A and B are open, their combined filling rate is the sum of their individual rates:
Combined filling rate = 1/15 + 1/20 = 4/60 + 3/60 = 7/60 of the tank per minute.
Now, let's determine the amount of water that has been filled in the tank after 4 minutes when pipe A is turned off:
In 4 minutes, both pipes A and B have been open, so the amount of water filled by both pipes is:
Amount filled in 4 minutes = (7/60) * 4 = 28/60 of the tank.
After 4 minutes, pipe A is turned off and only pipe B continues to fill the tank. We need to calculate how long it takes for pipe B to fill the remaining portion of the tank, which is 1 - 28/60 = 32/60 of the tank.
Since pipe B fills the tank at a rate of 1/20 of the tank per minute, the time it takes to fill the remaining portion of the tank is:
Time = (32/60)/(1/20) = (32/60) * (20/1) = 32/3 minutes.
Finally, to find the total time required to fill the tank, we add the time it took for both pipes to fill the tank initially (4 minutes) and the time it took for pipe B to fill the remaining portion (32/3 minutes):
Total time = 4 + 32/3 = 12 + 32/3 = 36/3 + 32/3 = 68/3 minutes.
Converting this to minutes and seconds:
Total time = 22 minutes and 40 seconds.
Therefore, the correct answer is option D) 14 minutes and 40 seconds.
A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:- a)49 m2
- b)50 m2
- c)53.5 m2
- d)55 m2
Correct answer is option 'A'. Can you explain this answer?
A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
a)
49 m2
b)
50 m2
c)
53.5 m2
d)
55 m2
|
|
Pranjal Banerjee answered |
Area of the wet surface
= [2(lb + bh + lh) – lb]
= 2(bh + lh) + lb
= [2 (4 × 1.25 + 6 × 1.25) + 6 × 4] m2
= 49 m2
= [2(lb + bh + lh) – lb]
= 2(bh + lh) + lb
= [2 (4 × 1.25 + 6 × 1.25) + 6 × 4] m2
= 49 m2
What is the capacity of the cylindrical tank?
I. The area of the base is 61,600 sq. cm.
II. The height of the tank is 1.5 times the radius.
III. The circumference of base is 880 cm.
- a)Only I and II
- b)Only II and III
- c)Only I and III
- d)Only II and either I or III
Correct answer is option 'D'. Can you explain this answer?
What is the capacity of the cylindrical tank?
I. The area of the base is 61,600 sq. cm.
II. The height of the tank is 1.5 times the radius.
III. The circumference of base is 880 cm.
I. The area of the base is 61,600 sq. cm.
II. The height of the tank is 1.5 times the radius.
III. The circumference of base is 880 cm.
a)
Only I and II
b)
Only II and III
c)
Only I and III
d)
Only II and either I or III
|
Sneha Khanna answered |
To determine the capacity of the cylindrical tank, we need to find the volume of the cylinder, which is given by the formula:
Volume=πr2h
Where:
- r is the radius of the base of the cylinder
- h is the height of the cylinder
- r is the radius of the base of the cylinder
- h is the height of the cylinder
Step 1: Analyze the Statements
1. Statement I: The area of the base is 61600sq. cm.
- The area of the base of a cylinder is given by the formula:
Area=πr2
- From this statement, we can find the radius r as follows:
- Thus, Statement I is necessary to find the radius.
- The area of the base of a cylinder is given by the formula:
Area=πr2
- From this statement, we can find the radius r as follows:
- Thus, Statement I is necessary to find the radius.
2. Statement II: The height of the tank is 1.5 times the radius.
- This gives us a direct relationship between height and radius:
h=1.5r
- Therefore, Statement II is also necessary to find the height.
- This gives us a direct relationship between height and radius:
h=1.5r
- Therefore, Statement II is also necessary to find the height.
3. Statement III: The circumference of the base is 880cm.
- The circumference of the base is given by:
Circumference=2πr
- From this statement, we can find the radius r as follows:
- Thus, Statement III is also necessary to find the radius.
- The circumference of the base is given by:
Circumference=2πr
- From this statement, we can find the radius r as follows:
- Thus, Statement III is also necessary to find the radius.
Step 2: Determine Necessary Statements
To calculate the volume of the cylinder, we need both the radius r and the height h.
- From Statement I, we can find the radius.
- From Statement II, we can find the height based on the radius.
- From Statement III, we can also find the radius.
- From Statement II, we can find the height based on the radius.
- From Statement III, we can also find the radius.
Conclusion
To determine the capacity of the cylindrical tank, we need:
- Statement I (Area of the base) or Statement III (Circumference of the base) to find the radius.
- Statement II (Height in terms of radius) is necessary to find the height.
- Statement I (Area of the base) or Statement III (Circumference of the base) to find the radius.
- Statement II (Height in terms of radius) is necessary to find the height.
Thus, the necessary statements to answer the question are:
- Statement II is essential, and either Statement I or Statement III is also required.
- Statement II is essential, and either Statement I or Statement III is also required.
Final Answer
The necessary statements are:
- Statement II (Height is 1.5 times the radius)
- Either Statement I (Area of the base) or Statement III (Circumference of the base).
- Statement II (Height is 1.5 times the radius)
- Either Statement I (Area of the base) or Statement III (Circumference of the base).
---
A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?- a)3 hrs 15 min
- b)3 hrs 45 min
- c)4 hrs
- d)4 hrs 15 min
Correct answer is option 'B'. Can you explain this answer?
A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
a)
3 hrs 15 min
b)
3 hrs 45 min
c)
4 hrs
d)
4 hrs 15 min
|
Ishaan Chakraborty answered |
Time taken by one tap to fill half of the tank = 3 hrs.
Part filled by the four taps in 1 hour
= (4 × 1/6) = 2/3
Remaining part = (1 – 1/2) = 1/2
∴ 2/3 : ½ :: 1 : x
⇒ x = (1/2 × 1 × 3/2) = 3/4 hours = 45 minutes
So, total time taken = 3 hrs. 45 minutes
Part filled by the four taps in 1 hour
= (4 × 1/6) = 2/3
Remaining part = (1 – 1/2) = 1/2
∴ 2/3 : ½ :: 1 : x
⇒ x = (1/2 × 1 × 3/2) = 3/4 hours = 45 minutes
So, total time taken = 3 hrs. 45 minutes
What is the height of a circular cone?
I. The area of that cone is equal to the area of a rectangle whose length is 33 cm.
II. The area of the base of that cone is 154 sq. cm.- a)I alone sufficient while II alone not sufficient to answer
- b)II alone sufficient while I alone not sufficient to answer
- c)Either I or II alone sufficient to answer
- d)Both I and II are not sufficient to answer
Correct answer is option 'D'. Can you explain this answer?
What is the height of a circular cone?
I. The area of that cone is equal to the area of a rectangle whose length is 33 cm.
II. The area of the base of that cone is 154 sq. cm.
I. The area of that cone is equal to the area of a rectangle whose length is 33 cm.
II. The area of the base of that cone is 154 sq. cm.
a)
I alone sufficient while II alone not sufficient to answer
b)
II alone sufficient while I alone not sufficient to answer
c)
Either I or II alone sufficient to answer
d)
Both I and II are not sufficient to answer
|
|
Jithin Chawla answered |
II gives the value of r.
But, in I, the breadth of rectangle is not given.
So, we cannot find the surface area of the cone.
Hence, the height of the cone cannot be determined.
∴ Correct answer is (d).
But, in I, the breadth of rectangle is not given.
So, we cannot find the surface area of the cone.
Hence, the height of the cone cannot be determined.
∴ Correct answer is (d).
What is the capacity of a cylindrical tank?
I. Radius of the base is half of its height which is 28 metres.
II. Area of the base is 616 sq. metres and its height is 28 metres.- a)I alone sufficient while II alone not sufficient to answer
- b)II alone sufficient while I alone not sufficient to answer
- c)Either I or II alone sufficient to answer
- d)Both I and II are not sufficient to answer
Correct answer is option 'C'. Can you explain this answer?
What is the capacity of a cylindrical tank?
I. Radius of the base is half of its height which is 28 metres.
II. Area of the base is 616 sq. metres and its height is 28 metres.
I. Radius of the base is half of its height which is 28 metres.
II. Area of the base is 616 sq. metres and its height is 28 metres.
a)
I alone sufficient while II alone not sufficient to answer
b)
II alone sufficient while I alone not sufficient to answer
c)
Either I or II alone sufficient to answer
d)
Both I and II are not sufficient to answer
|
|
Prateek Sharma answered |
From I, h = 28 m and r = 14.
∴ Capacity = π r2h, which can be obtained.
Thus, I alone gives the answer.
From II, π r2 = 616 m2 and h = 28 m
∴ Capacity = (π r2 × h) = (616 × 28) m3
Thus, II alone gives the answer.
∴ Correct answer is (c).
∴ Capacity = π r2h, which can be obtained.
Thus, I alone gives the answer.
From II, π r2 = 616 m2 and h = 28 m
∴ Capacity = (π r2 × h) = (616 × 28) m3
Thus, II alone gives the answer.
∴ Correct answer is (c).
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:- a)81 min.
- b)108 min.
- c)144 min.
- d)192 min.
Correct answer is option 'C'. Can you explain this answer?
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
a)
81 min.
b)
108 min.
c)
144 min.
d)
192 min.
|
|
Lakshmi Reddy answered |
Let the slower pipe alone fill the tank in x minutes.
Then, faster pipe will fill it in x/3 minutes.
1/x + 3/x = 1/36
⇒ 4/x = 1/36
⇒ x = 144 min.
Then, faster pipe will fill it in x/3 minutes.
1/x + 3/x = 1/36
⇒ 4/x = 1/36
⇒ x = 144 min.
Is a given rectangular block a cube?
I. At least 2 faces of the rectangular block are squares.
II. The volume of the block is 64.- a)I alone sufficient while II alone not sufficient to answer
- b)II alone sufficient while I alone not sufficient to answer
- c)Either I or II alone sufficient to answer
- d)Both I and II are not sufficient to answer
Correct answer is option 'D'. Can you explain this answer?
Is a given rectangular block a cube?
I. At least 2 faces of the rectangular block are squares.
II. The volume of the block is 64.
I. At least 2 faces of the rectangular block are squares.
II. The volume of the block is 64.
a)
I alone sufficient while II alone not sufficient to answer
b)
II alone sufficient while I alone not sufficient to answer
c)
Either I or II alone sufficient to answer
d)
Both I and II are not sufficient to answer
|
|
Rithika Roy answered |
From I, any two of l, b, h are equal.
From II, lbh = 64.
From I and II, the values of l, b, h may be (1, 1, 64), (2, 2, 16), (4, 4, 4).
Thus, the block may be a cube or cuboid.
∴ Correct answer is (d).
From II, lbh = 64.
From I and II, the values of l, b, h may be (1, 1, 64), (2, 2, 16), (4, 4, 4).
Thus, the block may be a cube or cuboid.
∴ Correct answer is (d).
In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:- a)75 cu. m
- b)750 cu. m
- c)7500 cu. m
- d)75000 cu. m
Correct answer is option 'B'. Can you explain this answer?
In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
a)
75 cu. m
b)
750 cu. m
c)
7500 cu. m
d)
75000 cu. m
|
|
Pranjal Banerjee answered |
1 hectare = 10,000 m2
So, Area = (1.5 × 10000) m2 = 15000 m2
Depth = (5/100) m = (1/20) m
∴ Volume = (Area × Depth)
= (15000 × 1/20) m3 = 750 m3
So, Area = (1.5 × 10000) m2 = 15000 m2
Depth = (5/100) m = (1/20) m
∴ Volume = (Area × Depth)
= (15000 × 1/20) m3 = 750 m3
Find the number of lead balls of diameter 1 cm each that can be made from a sphere of diameter 16 m.- a)4096
- b)2050
- c)3016
- d)5024
Correct answer is option 'A'. Can you explain this answer?
Find the number of lead balls of diameter 1 cm each that can be made from a sphere of diameter 16 m.
a)
4096
b)
2050
c)
3016
d)
5024
|
|
Shalini Menon answered |
Number of balls = Volume of big sphere /
Volume of one small sphere
= (4 π / 3 × 8 × 8 × 8)/
(4 π / 3 × 0.5 × 0.5 × 0.5)
= 4096
Volume of one small sphere
= (4 π / 3 × 8 × 8 × 8)/
(4 π / 3 × 0.5 × 0.5 × 0.5)
= 4096
The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs 5300, what is the length of the plot in metres?- a)40
- b)50
- c)120
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs 5300, what is the length of the plot in metres?
a)
40
b)
50
c)
120
d)
None of these
|
Pallabi Saha answered |
Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = (5300/26.50) m = 200 m
∴ 2[(x + 20) + x] = 200
⇒ 2x + 20 = 100
⇒ 2x = 80
⇒ x = 40
Hence, length = x + 20 = 60 m.
Then, length = (x + 20) metres.
Perimeter = (5300/26.50) m = 200 m
∴ 2[(x + 20) + x] = 200
⇒ 2x + 20 = 100
⇒ 2x = 80
⇒ x = 40
Hence, length = x + 20 = 60 m.
66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:- a)84 m
- b)90 m
- c)168 m
- d)336 m
Correct answer is option 'A'. Can you explain this answer?
66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:
a)
84 m
b)
90 m
c)
168 m
d)
336 m
|
|
Prateek Sharma answered |
Let the length of the wire be h.
Radius = 1/2 mm = 1/20 cm. Then,
⇒ (22/7 × 1/20 × 1/20 × h) = 66
∴ h = (60 × 20 × 20 × 7)/22 = 8400
cm = 84 m
Radius = 1/2 mm = 1/20 cm. Then,
⇒ (22/7 × 1/20 × 1/20 × h) = 66
∴ h = (60 × 20 × 20 × 7)/22 = 8400
cm = 84 m
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