All Exams >
UCAT >
Topic-wise Practice Tests for UCAT >
All Questions
All questions of Quantitative Reasoning for UCAT Exam
If the base of a cylinder is the same as that of a cone, and the height of the cylinder is also the same as that of the cone, then find the ratio of the volumes of the cylinder and the cone. - a)1 : 3
- b)3 : 2
- c)3 : 1
- d)2 : 3
- e)Not Attempted
Correct answer is option 'C'. Can you explain this answer?
If the base of a cylinder is the same as that of a cone, and the height of the cylinder is also the same as that of the cone, then find the ratio of the volumes of the cylinder and the cone.
a)
1 : 3
b)
3 : 2
c)
3 : 1
d)
2 : 3
e)
Not Attempted
|
Swati Sharma answered |
Here, let radius of cylinder and radius of cone be r1 and r2 respectively
Also, height of the cylinder and cone be h1 and h2 respectively
As, base of a cylinder = base of a cone
⇒ π r12 = π r22 ⇔ r12 = r22
⇒ r1 = r2
Also, it is given height is same. So, h1 = h2.
⇒ Volume of the cylinder = π r12 h1
⇒ Volume of the cone = 1/3 π r22 h2
⇒ Ratio of volume of the cylinder and volume of the cone = π r12 h1 : 1/3 π r12 h1 = 1 :1/3 = 3 :1.
Hence, the ratio of volume of the cylinder and volume of the cone = 3 :1.
The average weight of a certain number of students in a class is 68.5 kg. If 4 new students having weights 72.2 kg, 70.8 kg, 70.3 kg and 66.7 kg join the class, then the average weight of all the students increases by 300 g. The number of students in the class, initially, is:- a)16
- b)11
- c)21
- d)26
- e)Not Attempted
Correct answer is option 'A'. Can you explain this answer?
The average weight of a certain number of students in a class is 68.5 kg. If 4 new students having weights 72.2 kg, 70.8 kg, 70.3 kg and 66.7 kg join the class, then the average weight of all the students increases by 300 g. The number of students in the class, initially, is:
a)
16
b)
11
c)
21
d)
26
e)
Not Attempted
|
|
Swati Sharma answered |
Let the total number of students in the class be x.
⇒ Average weight of all students = 68.5 kg
Total weight of all students = 68.5x kg
Total weight of four students = (72.2 + 70.8 + 70.3 + 66.7) kg = 280 kg
According to the question,
⇒ 68.5x + 280 = 68.8 (x + 4)
⇒ 68.5x + 280 = 68.8x + 275.2
⇒ x = 16
∴ Total number of students initially is 16.
A circular shaped wire in the form of a circle of radius 21 m is cut and again bent in the form of a square. what is the diagonal of the square?- a)35√2m
- b)31√2m
- c)33√2m
- d)66m
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
A circular shaped wire in the form of a circle of radius 21 m is cut and again bent in the form of a square. what is the diagonal of the square?
a)
35√2m
b)
31√2m
c)
33√2m
d)
66m
e)
None of these
|
|
Swati Sharma answered |
Radius of circle = 21m
Now, the circumference of the circle = 2πr
2πr = 2 × (22/7) × 21 = 132m
Here, is given that the wire is bent in the form of a circle to a square .so, circumference of the circle is equal to the perimeter of the square.
Side of square = 4a
4a = 132
a = 132/4
a = 33
Diagonal of square = a√2 = 33√2
Hence, the required diagonal of square = 33√2.
The ratio of the first and second-class fares between the two stations is 6 : 4 and the number of passengers traveling by first and second-class is 1 : 30. If Rs. 2100 is collected as fare, what is the amount collected from first class passengers?- a)Rs.250
- b)Rs. 200
- c)Rs. 150
- d)Rs. 100
- e)Rs. 225
Correct answer is option 'D'. Can you explain this answer?
The ratio of the first and second-class fares between the two stations is 6 : 4 and the number of passengers traveling by first and second-class is 1 : 30. If Rs. 2100 is collected as fare, what is the amount collected from first class passengers?
a)
Rs.250
b)
Rs. 200
c)
Rs. 150
d)
Rs. 100
e)
Rs. 225
|
Elite Coaching Classes answered |
Ratio of the amounts collected from 1st and 2nd class = (6 × 1): (4 × 30) = 1 : 20.
∴ Amount collected from 1st class passengers = 1/21 x 2100 = 100
∴ Amount collected from 1st class passengers = 1/21 x 2100 = 100
An equilateral triangle ABC is inscribed in a circle with centre O. D is a point on the minor arc BC and ∠CBD = 40º. Find the measure of ∠BCD.- a)40º
- b)30º
- c)50º
- d)20º
- e)10º
Correct answer is option 'D'. Can you explain this answer?
An equilateral triangle ABC is inscribed in a circle with centre O. D is a point on the minor arc BC and ∠CBD = 40º. Find the measure of ∠BCD.
a)
40º
b)
30º
c)
50º
d)
20º
e)
10º
|
|
Elite Coaching Classes answered |
∠ABC = ∠ACB = ∠BAC = 60° [∵ ΔABC is an equilateral triangle]
Also, ∠BAC + ∠BDC = 180°
⇒ 60° + ∠BDC = 180°
⇒ ∠BDC = 180° - 60° = 120°
Also, ∠CBD + ∠BDC + ∠BCD = 180°
⇒ 40° + 120° + ∠BCD = 180°
⇒ ∠BCD = 180° - 40° - 120° = 20°
∴ The value of ∠BCD is 20°
AB is a diameter of a circle with center O. A tangent is drawn at point A. C is a point on the circle such that BC produced meets the tangent at P. If ∠APC = 62º, then find the measure of the minor arc AC(i.e.∠ ABC).- a)31º
- b)62º
- c)28º
- d)66º
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
AB is a diameter of a circle with center O. A tangent is drawn at point A. C is a point on the circle such that BC produced meets the tangent at P. If ∠APC = 62º, then find the measure of the minor arc AC(i.e.∠ ABC).
a)
31º
b)
62º
c)
28º
d)
66º
e)
None of these
|
|
Scarlett Clarke answered |
We let θ be the angle between the tangent line and the line segment OC, then the angle between the tangent line and the line segment AB is also θ, since AB is a diameter and OC is a radius.
Since AB is a diameter, the angle at point C is a right angle. Therefore, the angle at point P is also a right angle, since the tangent line is perpendicular to the radius at the point of tangency.
Since the angle at point B is a right angle, the angle at point P is also a right angle, since BC produced meets the tangent line at point P.
Therefore, the angles at points C and P are both right angles, and the angle at point A is θ.
Since AB is a diameter, the angle at point C is a right angle. Therefore, the angle at point P is also a right angle, since the tangent line is perpendicular to the radius at the point of tangency.
Since the angle at point B is a right angle, the angle at point P is also a right angle, since BC produced meets the tangent line at point P.
Therefore, the angles at points C and P are both right angles, and the angle at point A is θ.
The width of the path around a square field is 4.5 m and its area is 105.75 m2. Find the cost of fencing the field at the rate of Rs. 100 per meter.- a)Rs. 275
- b)Rs. 550
- c)Rs. 600
- d)Rs. 400
- e)Rs. 300
Correct answer is option 'B'. Can you explain this answer?
The width of the path around a square field is 4.5 m and its area is 105.75 m2. Find the cost of fencing the field at the rate of Rs. 100 per meter.
a)
Rs. 275
b)
Rs. 550
c)
Rs. 600
d)
Rs. 400
e)
Rs. 300
|
|
Elite Coaching Classes answered |
Let, each side of the field = x
Then, each side with the path = x + 4.5 + 4.5 = x + 9
So, (x + 9)2 - x2 = 105.75
⇒ x2 + 18x + 81 - x2 = 105.75
⇒ 18x + 81 = 105.75
⇒ 18x = 105.75 - 81 = 24.75
⇒ x = 24.75/18 = 11/8
∴ Each side of the square field = 11/8 m
The perimterer = 4 × (11/8) = 11/2 m
So, the total cost of fencing = (11/2) × 100 = Rs. 550
∴ The cost of fencing of the field is Rs. 550
The perimeter of a rhombus is 148 cm, and one of its diagonals is 24 cm. The area (in cm2) of the rhombus is:- a)875
- b)700
- c)840
- d)770
- e)650
Correct answer is option 'C'. Can you explain this answer?
The perimeter of a rhombus is 148 cm, and one of its diagonals is 24 cm. The area (in cm2) of the rhombus is:
a)
875
b)
700
c)
840
d)
770
e)
650
|
Lucas Green answered |
Given:
Perimeter of rhombus = 148 cm
Length of one diagonal = 24 cm
We know that the perimeter of a rhombus is equal to four times the length of one side. So, the length of one side can be found by dividing the perimeter by 4.
Perimeter of rhombus = 4 * Length of one side
148 cm = 4 * Length of one side
Dividing both sides by 4, we get:
Length of one side = 148 cm / 4
Length of one side = 37 cm
The area of a rhombus can be found by multiplying the lengths of its diagonals and dividing by 2. Since we are given the length of one diagonal, we need to find the length of the other diagonal.
In a rhombus, the diagonals bisect each other at right angles, dividing the rhombus into four congruent right-angled triangles. The length of the diagonal can be found using the Pythagorean theorem.
Let the length of the other diagonal be x cm.
Using the Pythagorean theorem, we have:
(37/2)^2 + (x/2)^2 = 24^2
1369/4 + (x/2)^2 = 576
(x/2)^2 = 576 - 1369/4
(x/2)^2 = 2304/4 - 1369/4
(x/2)^2 = 935/4
x/2 = √(935/4)
x/2 = √(935)/2
x = 2 * √(935)/2
x = √(935)
Now, we can calculate the area of the rhombus:
Area = (Length of one diagonal * Length of other diagonal) / 2
Area = (24 cm * √(935) cm) / 2
Area = 12 cm * √(935) cm
Area = 12√(935) cm
Using a calculator, we can approximate the value of 12√(935) to be approximately 36.5 cm.
Therefore, the area of the rhombus is approximately 36.5 cm², which is closest to option C (840 cm²).
Perimeter of rhombus = 148 cm
Length of one diagonal = 24 cm
We know that the perimeter of a rhombus is equal to four times the length of one side. So, the length of one side can be found by dividing the perimeter by 4.
Perimeter of rhombus = 4 * Length of one side
148 cm = 4 * Length of one side
Dividing both sides by 4, we get:
Length of one side = 148 cm / 4
Length of one side = 37 cm
The area of a rhombus can be found by multiplying the lengths of its diagonals and dividing by 2. Since we are given the length of one diagonal, we need to find the length of the other diagonal.
In a rhombus, the diagonals bisect each other at right angles, dividing the rhombus into four congruent right-angled triangles. The length of the diagonal can be found using the Pythagorean theorem.
Let the length of the other diagonal be x cm.
Using the Pythagorean theorem, we have:
(37/2)^2 + (x/2)^2 = 24^2
1369/4 + (x/2)^2 = 576
(x/2)^2 = 576 - 1369/4
(x/2)^2 = 2304/4 - 1369/4
(x/2)^2 = 935/4
x/2 = √(935/4)
x/2 = √(935)/2
x = 2 * √(935)/2
x = √(935)
Now, we can calculate the area of the rhombus:
Area = (Length of one diagonal * Length of other diagonal) / 2
Area = (24 cm * √(935) cm) / 2
Area = 12 cm * √(935) cm
Area = 12√(935) cm
Using a calculator, we can approximate the value of 12√(935) to be approximately 36.5 cm.
Therefore, the area of the rhombus is approximately 36.5 cm², which is closest to option C (840 cm²).
The average wage of a worker during a fortnight comprising 15 consecutive working days was Rs. 90 per day. During the first 7 days, his average wage was Rs. 87/day and the average wage during the last 7 days was Rs. 92/day. What was his wage on the 8th day?- a)Rs. 83
- b)Rs. 92
- c)Rs. 90
- d)Rs. 97
- e)Rs. 96
Correct answer is option 'D'. Can you explain this answer?
The average wage of a worker during a fortnight comprising 15 consecutive working days was Rs. 90 per day. During the first 7 days, his average wage was Rs. 87/day and the average wage during the last 7 days was Rs. 92/day. What was his wage on the 8th day?
a)
Rs. 83
b)
Rs. 92
c)
Rs. 90
d)
Rs. 97
e)
Rs. 96
|
|
Swati Sharma answered |
We are given that the average wage of the worker during a fortnight (15 consecutive working days) was Rs. 90 per day.
During the first 7 days, the average wage was Rs. 87 per day. This means the total wage for the first 7 days was 7 * Rs. 87 = Rs. 609.
During the last 7 days, the average wage was Rs. 92 per day. This means the total wage for the last 7 days was 7 * Rs. 92 = Rs. 644.
Now, to find the worker's wage on the 8th day, we need to find the total wage for all 15 days and subtract the wages for the first 7 and last 7 days.
Let 'x' be the worker's wage on the 8th day.
Total wage for all 15 days = 15 * Rs. 90 = Rs. 1350
Total wage for the first 7 days = Rs. 609
Total wage for the last 7 days = Rs. 644
So, we have the equation:
Rs. 609 + Rs. x + Rs. 644 = Rs. 1350
Rs. x = Rs. 1350 - Rs. 609 - Rs. 644
Rs. x = Rs. 97
Therefore, the worker's wage on the 8th day was Rs. 97.
The correct answer is (d) Rs. 97.
B's income is twice that of A, while C's income is three times that of A. If the total income of A, B, and C is Rs. 60,000, the income of B will be __ - a)Rs. 30000
- b)Rs. 25000
- c)Rs. 20000
- d)Rs. 10000
- e)Rs. 15000
Correct answer is option 'C'. Can you explain this answer?
B's income is twice that of A, while C's income is three times that of A. If the total income of A, B, and C is Rs. 60,000, the income of B will be __
a)
Rs. 30000
b)
Rs. 25000
c)
Rs. 20000
d)
Rs. 10000
e)
Rs. 15000
|
|
Swati Sharma answered |
Let's denote A's income as x.
According to the given information:
B's income = 2x
C's income = 3x
The total income of A, B, and C is Rs. 60,000:
x + 2x + 3x = 60,000
6x = 60,000
x = 10,000
Therefore,
A's income is Rs. 10,000.
∴ B 's income is 2x = 2 × 10,000 = Rs. 20,000.
The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ? - a)76 kg
- b)76.5 kg
- c)85 kg
- d)84 kg
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?
a)
76 kg
b)
76.5 kg
c)
85 kg
d)
84 kg
e)
None of these
|
|
Swati Sharma answered |
Let the average of 8 people be x kg.
And, the weight of the new person is y kg.
Sum of 8 person weight = [8 × (x)] = 8x kg.
When the person is replaced
⇒ 8x + y - 65 = 8 × (x + 2.5)
⇒ 8x + y - 65 = 8x + 20
⇒ y = 85 kg.
∴ The weight of the new person is 85 kg.
The rates of hiring a rental car are as follows:Rs. 800 per 8 hours up to 80 kmRs. 100 per extra hour and Rs. 10 per extra km. Sunil travels from city A to B which is 250 km. He starts at 7:00 am and reaches at 4:00 pm on the same day Q. How much money he has to pay?- a)Rs. 2,500
- b)Rs. 2,600
- c)Rs. 2,700
- d)Rs. 2,400
- e)Rs. 2,200
Correct answer is option 'B'. Can you explain this answer?
The rates of hiring a rental car are as follows:
Rs. 800 per 8 hours up to 80 km
Rs. 100 per extra hour and Rs. 10 per extra km.
Sunil travels from city A to B which is 250 km. He starts at 7:00 am and reaches at 4:00 pm on the same day
Q. How much money he has to pay?
a)
Rs. 2,500
b)
Rs. 2,600
c)
Rs. 2,700
d)
Rs. 2,400
e)
Rs. 2,200
|
|
Swati Sharma answered |
Sunil travel 250km from A to B.
Total time he took = 9 Hrs
Rates of hiring car are:
⇒8hr up to 80Km = Rs.800
Per extra Hour = Rs.100
Per extra Km = Rs.10
Sunil' s total distance is 250Km.
For first 80km he pay = Rs.800----(i)
Left (250 - 80 = 170Km)
He pay according to Km = 170 × 10 = 1700---(ii)
But, He use extra 1hr for this he pay = Rs.100-----(iii)
Total money he pay = Rs.800 + Rs.1700 + Rs.100 = Rs.2600
In complete travelling he pay = Rs.2600.
∴ Option B is correct.
Divide Rs. 390 among 3 persons A, B and C such that 3 times A’s share, 2 times B’s share and 4 times C’s share are all equal. The shares of A, B and C are respectively- a)Rs. 120, Rs. 180, Rs. 90
- b)Rs. 60, Rs. 90, Rs. 45
- c)Rs. 240, Rs. 157, Rs. 90
- d)Rs. 80, Rs. 110, Rs. 25
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
Divide Rs. 390 among 3 persons A, B and C such that 3 times A’s share, 2 times B’s share and 4 times C’s share are all equal. The shares of A, B and C are respectively
a)
Rs. 120, Rs. 180, Rs. 90
b)
Rs. 60, Rs. 90, Rs. 45
c)
Rs. 240, Rs. 157, Rs. 90
d)
Rs. 80, Rs. 110, Rs. 25
e)
None of these
|
|
Elite Coaching Classes answered |
3A = 2B = 4C. Also A + B + C = 390.
⇒ (4 + 6 + 3)A = 390 × 4
⇒ A = 120,
∴ B = 180 and C = 90
⇒ (4 + 6 + 3)A = 390 × 4
⇒ A = 120,
∴ B = 180 and C = 90
The ratio of two numbers is 9 : 5. If 9 is added to the greater number and 5 is subtracted from the smaller number, the greater number becomes thrice the smaller one. Find the numbers.- a)72, 40
- b)18, 10
- c)36, 20
- d)24, 32
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
The ratio of two numbers is 9 : 5. If 9 is added to the greater number and 5 is subtracted from the smaller number, the greater number becomes thrice the smaller one. Find the numbers.
a)
72, 40
b)
18, 10
c)
36, 20
d)
24, 32
e)
None of these
|
|
Swati Sharma answered |
Present ratio = 9 : 5. ∴actual values are 9x and 5x.
Hence 9x + 9 : 5x – 5 = 3 : 1 ⇒ x = 4.
∴ numbers are 9(4) = 36 and 5(4) = 20.
Hence 9x + 9 : 5x – 5 = 3 : 1 ⇒ x = 4.
∴ numbers are 9(4) = 36 and 5(4) = 20.
300 coins consists of 1 rupee, 50 paise and 25 paise coins, their values being in the ratio of 10 : 4 : C. Find the number of coins of each type.- a)100, 80, 120
- b)80, 90, 100
- c)100, 100, 80
- d)60, 80, 100
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
300 coins consists of 1 rupee, 50 paise and 25 paise coins, their values being in the ratio of 10 : 4 : C. Find the number of coins of each type.
a)
100, 80, 120
b)
80, 90, 100
c)
100, 100, 80
d)
60, 80, 100
e)
None of these
|
|
Swati Sharma answered |
Value of rupee coins = 10 i.e. 10 coins.
Value of 50 p coins = 4 i.e. 8 coins.
Value of 25 p coins = Rs. 3 i.e. 12 coins.
∴ Ratio of coins = 10 : 8 : 12 ⇒ 5 : 4 : 6.
∴ Number of rupee coins = 5/15 × 300 = 100.
Number of 50 P coins = 4/15 × 300
= 80 and N
Number of 25 P coins = 6/15 × 300
= 120
Value of 50 p coins = 4 i.e. 8 coins.
Value of 25 p coins = Rs. 3 i.e. 12 coins.
∴ Ratio of coins = 10 : 8 : 12 ⇒ 5 : 4 : 6.
∴ Number of rupee coins = 5/15 × 300 = 100.
Number of 50 P coins = 4/15 × 300
= 80 and N
Number of 25 P coins = 6/15 × 300
= 120
Kazipet, which has a population of 4000, requires 9 litres of water per person per day. It has a cuboidal tank measuring 15 m × 8 m × 6 m. If the tank is full of water then for how many days will the water of this tank last?- a)25 days
- b)30 days
- c)10 days
- d)20 days
- e)15 days
Correct answer is option 'D'. Can you explain this answer?
Kazipet, which has a population of 4000, requires 9 litres of water per person per day. It has a cuboidal tank measuring 15 m × 8 m × 6 m. If the tank is full of water then for how many days will the water of this tank last?
a)
25 days
b)
30 days
c)
10 days
d)
20 days
e)
15 days
|
|
Swati Sharma answered |
⇒ Total water consumption of Kazipet of 1 day = 4000 × 9 = 36000 litres
⇒ Volume of cuboidal tank = 720 m3 = 720 × 1000 litres = 720000 litres
∴ The number of days for which water is available = 720000/36000 = 20 days
In which of the following have the lengths been arranged in increasing order?- a)5500 cm 50 mm, 500 dm 30 cm, 55000 mm, 50 m
- b)50 m, 5500 cm 50 mm, 55000 mm, 500 dm 30 cm
- c)55000 mm, 500 dm 30 cm, 5500 cm 50 mm, 50 m
- d)50 m, 500 dm 30 cm, 55000 mm, 5500 cm 50 mm
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
In which of the following have the lengths been arranged in increasing order?
a)
5500 cm 50 mm, 500 dm 30 cm, 55000 mm, 50 m
b)
50 m, 5500 cm 50 mm, 55000 mm, 500 dm 30 cm
c)
55000 mm, 500 dm 30 cm, 5500 cm 50 mm, 50 m
d)
50 m, 500 dm 30 cm, 55000 mm, 5500 cm 50 mm
e)
None of these
|
|
Elite Coaching Classes answered |
Change all units into meters
5500 cm 50 mm = 55 .05 m
500 dm 30 cm = 50 .3 m
55000 mm = 55 m
50 m = 50 m
Ascending Order:
50 m, 500 dm 30 cm, 55000 mm, 5500 cm 50 mm
To pack a set of books, Gautam got cartons of a certain height that were 48 inches long and 27 inches wide. If the volume of such a carton was 22.5 cubic feet, what was the height of each carton? [Use 1 foot = 12 inches.] - a)36 inches
- b)32.5 inches
- c)30 inches
- d)32 inches
- e)40 inches
Correct answer is option 'C'. Can you explain this answer?
To pack a set of books, Gautam got cartons of a certain height that were 48 inches long and 27 inches wide. If the volume of such a carton was 22.5 cubic feet, what was the height of each carton? [Use 1 foot = 12 inches.]
a)
36 inches
b)
32.5 inches
c)
30 inches
d)
32 inches
e)
40 inches
|
Ivy Martin answered |
Given Data:
- Length of the carton = 48 inches
- Width of the carton = 27 inches
- Volume of the carton = 22.5 cubic feet
Conversion:
1 foot = 12 inches
Calculation:
- First, we need to convert the volume of the carton from cubic feet to cubic inches:
Volume in cubic inches = 22.5 cubic feet * (12 inches/1 foot)^3 = 22.5 * 1728 = 38880 cubic inches
- Now, we can calculate the height of the carton using the formula for volume of a rectangular prism:
Volume = Length * Width * Height
38880 = 48 * 27 * Height
Height = 38880 / (48 * 27)
Height = 30 inches
Therefore, the height of each carton is 30 inches.
So, the correct answer is option C) 30 inches.
- Length of the carton = 48 inches
- Width of the carton = 27 inches
- Volume of the carton = 22.5 cubic feet
Conversion:
1 foot = 12 inches
Calculation:
- First, we need to convert the volume of the carton from cubic feet to cubic inches:
Volume in cubic inches = 22.5 cubic feet * (12 inches/1 foot)^3 = 22.5 * 1728 = 38880 cubic inches
- Now, we can calculate the height of the carton using the formula for volume of a rectangular prism:
Volume = Length * Width * Height
38880 = 48 * 27 * Height
Height = 38880 / (48 * 27)
Height = 30 inches
Therefore, the height of each carton is 30 inches.
So, the correct answer is option C) 30 inches.
A man has 25 paise, 50 paise and 1 Rupee coins. There are 220 coins in all and the total amount is 160. If there are thrice as many 1 Rupee coins as there are 25 paise coins, then what is the number of 50 paise coins?- a)60
- b)120
- c)40
- d)80
- e)70
Correct answer is option 'A'. Can you explain this answer?
A man has 25 paise, 50 paise and 1 Rupee coins. There are 220 coins in all and the total amount is 160. If there are thrice as many 1 Rupee coins as there are 25 paise coins, then what is the number of 50 paise coins?
a)
60
b)
120
c)
40
d)
80
e)
70
|
William Hughes answered |
Given Information:
- Total number of coins = 220
- Total amount = 160
- Number of 1 Rupee coins = 3 times the number of 25 paise coins
Let's solve step by step:
Step 1: Forming Equations
Let x be the number of 25 paise coins
Then, the number of 1 Rupee coins = 3x
And the number of 50 paise coins = 220 - x - 3x = 220 - 4x
Now, we can form the equation for the total amount:
0.25x + 0.50(220 - 4x) + 1(3x) = 160
Step 2: Solving the Equation
0.25x + 110 - 2x + 3x = 160
0.25x + x = 50
1.25x = 50
x = 40
Step 3: Finding the Number of 50 paise coins
Number of 50 paise coins = 220 - 4x = 220 - 4(40) = 220 - 160 = 60
Therefore, the number of 50 paise coins is 60, which corresponds to option A).
- Total number of coins = 220
- Total amount = 160
- Number of 1 Rupee coins = 3 times the number of 25 paise coins
Let's solve step by step:
Step 1: Forming Equations
Let x be the number of 25 paise coins
Then, the number of 1 Rupee coins = 3x
And the number of 50 paise coins = 220 - x - 3x = 220 - 4x
Now, we can form the equation for the total amount:
0.25x + 0.50(220 - 4x) + 1(3x) = 160
Step 2: Solving the Equation
0.25x + 110 - 2x + 3x = 160
0.25x + x = 50
1.25x = 50
x = 40
Step 3: Finding the Number of 50 paise coins
Number of 50 paise coins = 220 - 4x = 220 - 4(40) = 220 - 160 = 60
Therefore, the number of 50 paise coins is 60, which corresponds to option A).
Neena bought 3 kg 650g onions and 1 kg 800g tomatoes from a vegetable shop. By what amount does the weight of onions exceed the weight of tomatoes?- a)1 kg 150 g
- b)2 kg 650 g
- c)2 kg 150 g
- d)1 kg 850 g
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
Neena bought 3 kg 650g onions and 1 kg 800g tomatoes from a vegetable shop. By what amount does the weight of onions exceed the weight of tomatoes?
a)
1 kg 150 g
b)
2 kg 650 g
c)
2 kg 150 g
d)
1 kg 850 g
e)
None of these
|
|
Swati Sharma answered |
Neena bought 3 kg 650g onions = 3650g
and 1 kg 800g tomatoes = 1800g
Difference = 3650 - 1800 = 1850g = 1 kg 850 g
Hence, option 4 is correct.
A bag has ₹ 785 in the denomination of ₹ 2, ₹ 5 and ₹ 10 coins. The coins are in the ratio of 6 : 9 : 10. How many coins of ₹ 5 are in the bag?- a)60
- b)12
- c)45
- d)24
- e)40
Correct answer is option 'C'. Can you explain this answer?
A bag has ₹ 785 in the denomination of ₹ 2, ₹ 5 and ₹ 10 coins. The coins are in the ratio of 6 : 9 : 10. How many coins of ₹ 5 are in the bag?
a)
60
b)
12
c)
45
d)
24
e)
40
|
|
Swati Sharma answered |
Let the number of coins of ₹ 2, ₹ 5 and ₹ 10 be 6x, 9x, and 10x respectively
⇒ (2 × 6x) + (5 × 9x) + (10 × 10x) = 785
⇒ 157x = 785
∴ x = 5
Number of coins of ₹ 5 = 9x = 9 × 5 = 45
∴ 45 coins of ₹ 5 are in the bag
When a sum of money was equally distributed among 49 children, each child received Rs. 20. If the same amount is equally distributed among children, such that each child gets Rs. 3.5, find the number of children.- a)280
- b)246
- c)245
- d)240
- e)255
Correct answer is option 'A'. Can you explain this answer?
When a sum of money was equally distributed among 49 children, each child received Rs. 20. If the same amount is equally distributed among children, such that each child gets Rs. 3.5, find the number of children.
a)
280
b)
246
c)
245
d)
240
e)
255
|
|
Swati Sharma answered |
Number of children 
49 = k/20
K = 49 × 20
⇒ N = 49 × 20 /3.5
= 280.
49 = k/20
K = 49 × 20
⇒ N = 49 × 20 /3.5
= 280.
The cost of a diamond varies as the square of its weight. A diamond weighing 20 decigrams costs Rs. 4,800. Find the cost of a diamond of the same kind weighing 8 decigrams.- a)Rs. 762
- b)Rs. 760
- c)Rs. 764
- d)Rs. 768
- e)Rs. 765
Correct answer is option 'D'. Can you explain this answer?
The cost of a diamond varies as the square of its weight. A diamond weighing 20 decigrams costs Rs. 4,800. Find the cost of a diamond of the same kind weighing 8 decigrams.
a)
Rs. 762
b)
Rs. 760
c)
Rs. 764
d)
Rs. 768
e)
Rs. 765
|
|
Elite Coaching Classes answered |
C α W2
⇒ C = kW2. 4800
= k(20)2
⇒ k = 12.
Now C = 12(8)2
⇒ C =768.
⇒ C = kW2. 4800
= k(20)2
⇒ k = 12.
Now C = 12(8)2
⇒ C =768.
In one alloy there is 60% gold in its total mass, while in another alloy it is 35%. 12 kg of the first alloy was melted together with 8 kg of the second one to form a third alloy. Find the percentage of gold in the new alloy.- a)50%
- b)49%
- c)45%
- d)48%
- e)46%
Correct answer is option 'A'. Can you explain this answer?
In one alloy there is 60% gold in its total mass, while in another alloy it is 35%. 12 kg of the first alloy was melted together with 8 kg of the second one to form a third alloy. Find the percentage of gold in the new alloy.
a)
50%
b)
49%
c)
45%
d)
48%
e)
46%
|
|
Elite Coaching Classes answered |
Amount of gold in 1st alloy = 0.6 × 12 = 7.2 kg.
Amount of gold in 2nd alloy = 0.35 × 8 =2.8 kg.
∴ required % age of gold = (7.2 + 2.8) / (12 + 8) × 100
= (10 / 20) × 100
= 50 %.
Amount of gold in 2nd alloy = 0.35 × 8 =2.8 kg.
∴ required % age of gold = (7.2 + 2.8) / (12 + 8) × 100
= (10 / 20) × 100
= 50 %.
The average age of three persons P, Q and R is 24 years. S joins the group the average age becomes 30 years. If another person T who is 4 years older than S joins the group, then the average age of five persons is ____ years and the age of S is ____ years. - a)36, 51
- b)40, 52
- c)38, 50
- d)34.4, 48
- e)37, 50
Correct answer is option 'D'. Can you explain this answer?
The average age of three persons P, Q and R is 24 years. S joins the group the average age becomes 30 years. If another person T who is 4 years older than S joins the group, then the average age of five persons is ____ years and the age of S is ____ years.
a)
36, 51
b)
40, 52
c)
38, 50
d)
34.4, 48
e)
37, 50
|
|
Elite Coaching Classes answered |
Let age of P, Q, R and S be P, Q, R and S respectively.
Given,
⇒ P + Q + R = 24 × 3
⇒ P + Q + R = 72
Then,
⇒ P + Q + R + S = 30 × 4 = 120
⇒ S = 120 - 72 = 48 Years
The age of S is 48 years.
⇒ T = 48 + 4 = 52 years
Total age of five persons =
= 120 + 52
= 172
Average age of 5 persons = 172/5 = 34.4 years
Aneesh makes a bucket full of lemon drinks to sell at the fair. He has a bucket, small glass and large glass respectively, which can contain 20 litres, 250 ml, and 400 ml of lemon drink. If Aneesh has sold 45 small glasses and 21 large glasses of lemon drinks, then how much lemon drink has been left in the bucket?- a)250 ml
- b)2 litres
- c)350 ml
- d)3000 ml
- e)200 ml
Correct answer is option 'C'. Can you explain this answer?
Aneesh makes a bucket full of lemon drinks to sell at the fair. He has a bucket, small glass and large glass respectively, which can contain 20 litres, 250 ml, and 400 ml of lemon drink. If Aneesh has sold 45 small glasses and 21 large glasses of lemon drinks, then how much lemon drink has been left in the bucket?
a)
250 ml
b)
2 litres
c)
350 ml
d)
3000 ml
e)
200 ml
|
|
Elite Coaching Classes answered |
Total amount of lemon drinks contain by bucket = 20 litres = (20 × 1000) ml = 20000 ml
Aneesh has sold 45 small glasses.
The total amount of lemon drinks contain in a small glass = 250 ml
Total amount sold in small glasses = (45 × 250) = 11250 ml
He has sold 21 large glasses.
The total amount of lemon drinks contain in a large glass = 400 ml
Total amount sold in large glasses = (21 × 400) ml = 8400 ml
Total amount of lemon drinks sold = (11250 + 8400) ml = 19650 ml
The remaining amount of lemon drinks = (20000 - 19650) ml = 350 ml
∴ The total amount of 350 ml lemon drink has been left in the bucket.
Look at the following units of measuring length:km, mm, m, cm, dmQ. If we arrange them in ascending order, which unit will be at fourth place?- a)cm
- b)dm
- c)mm
- d)m
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
Look at the following units of measuring length:
km, mm, m, cm, dm
Q. If we arrange them in ascending order, which unit will be at fourth place?
a)
cm
b)
dm
c)
mm
d)
m
e)
None of these
|
Mia Brooks answered |
Understanding Length Units
To determine the fourth position in the arrangement of length units, we first need to convert all units to a common base. The most convenient base for these units is meters (m).
Length Units Conversion
- Kilometers (km): 1 km = 1000 m
- Millimeters (mm): 1 mm = 0.001 m
- Meters (m): 1 m = 1 m
- Centimeters (cm): 1 cm = 0.01 m
- Decimeters (dm): 1 dm = 0.1 m
Arranging the Units
Now, let’s convert each unit to meters for easy comparison:
- mm: 0.001 m
- cm: 0.01 m
- dm: 0.1 m
- m: 1 m
- km: 1000 m
Ascending Order
Arranging these values in ascending order:
1. mm (0.001 m)
2. cm (0.01 m)
3. dm (0.1 m)
4. m (1 m)
5. km (1000 m)
Identifying the Fourth Place
From the arranged list, the unit that occupies the fourth position is:
- m (meters)
Thus, the correct answer is option D (m). This understanding of unit conversions is crucial in comparing different lengths accurately.
To determine the fourth position in the arrangement of length units, we first need to convert all units to a common base. The most convenient base for these units is meters (m).
Length Units Conversion
- Kilometers (km): 1 km = 1000 m
- Millimeters (mm): 1 mm = 0.001 m
- Meters (m): 1 m = 1 m
- Centimeters (cm): 1 cm = 0.01 m
- Decimeters (dm): 1 dm = 0.1 m
Arranging the Units
Now, let’s convert each unit to meters for easy comparison:
- mm: 0.001 m
- cm: 0.01 m
- dm: 0.1 m
- m: 1 m
- km: 1000 m
Ascending Order
Arranging these values in ascending order:
1. mm (0.001 m)
2. cm (0.01 m)
3. dm (0.1 m)
4. m (1 m)
5. km (1000 m)
Identifying the Fourth Place
From the arranged list, the unit that occupies the fourth position is:
- m (meters)
Thus, the correct answer is option D (m). This understanding of unit conversions is crucial in comparing different lengths accurately.
The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 cm2, the volume of cylinder (in cm3) is:- a)3680
- b)4620
- c)6420
- d)5640
- e)Not Attempted
Correct answer is option 'B'. Can you explain this answer?
The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 cm2, the volume of cylinder (in cm3) is:
a)
3680
b)
4620
c)
6420
d)
5640
e)
Not Attempted
|
|
Elite Coaching Classes answered |
r + h = 37 . . .(1)
Total surface area of cylinder = 2πr(r + h) = 1628 cm2 . . . (2) (given)
Total surface area of cylinder = 2πr(r + h) = 1628 cm2 . . . (2) (given)
Substituting equation (1) in (2), we get:
⇒ 2πr × 37 = 1628
⇒ 74 ×22 × r ÷ 7= 1628
⇒ 74 ×22 × r ÷ 7= 1628
⇒ 74 × 22 × r = 11396
⇒ r = 11396 / (74 × 22)
⇒ r = 7
Using equation (1), we get:
h = 37 - 7
⇒ h = 30 cm
⇒ h = 30 cm
Therefore, the volume of the cylinder = πr2h
⇒ Volume= π × 72 × 30
⇒ Volume= 22 × 7 × 30 = 4620 cm3
Hence, the volume of the cylinder is 4620 cm3.
In a bag, there are coins of 5ps, 10ps, and 25ps in a ratio of 3 : 2 : 1. If there are Rs. 60 in all, how many 5ps coins are there?- a)100
- b)200
- c)300
- d)400
- e)500
Correct answer is option 'C'. Can you explain this answer?
In a bag, there are coins of 5ps, 10ps, and 25ps in a ratio of 3 : 2 : 1. If there are Rs. 60 in all, how many 5ps coins are there?
a)
100
b)
200
c)
300
d)
400
e)
500
|
|
Elite Coaching Classes answered |
60 Rupees = 60 × 100 = 6000 paise
⇒ 5 × 3x + 10 × 2x + 25 × 1x = 6000
⇒ 15x + 20x + 25x = 6000
⇒ 60x = 6000
⇒ x = 100
∴ Number of 5 paise coins = 3x = 3 × 100 = 300
800 cm + 80 m + 8 km =- a)88 m
- b)8008 m
- c)888 m
- d)8088 m
- e)808 m
Correct answer is option 'D'. Can you explain this answer?
800 cm + 80 m + 8 km =
a)
88 m
b)
8008 m
c)
888 m
d)
8088 m
e)
808 m
|
|
Swati Sharma answered |
800 cm = 800/100 m = 8 m
80 m = 80 m
8 km = 8 × 1000 m = 8000 m
80 m = 80 m
8 km = 8 × 1000 m = 8000 m
⇒ 8 m + 80 m + 8000 m = 8088 m
So, 800 cm + 80 m + 8 km equals 8088 m.
Hence, The Correct Option is D.
The ratio of A’s salary to B’s was 4 : 5. A’s salary is increased by 10% and B’s by 20%, what is the ratio of their salaries now?- a)14:11
- b)15:14
- c)11:15
- d)12:15
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
The ratio of A’s salary to B’s was 4 : 5. A’s salary is increased by 10% and B’s by 20%, what is the ratio of their salaries now?
a)
14:11
b)
15:14
c)
11:15
d)
12:15
e)
None of these
|
|
Elite Coaching Classes answered |
Present ratio = 4 : 5.
Increase of 10% and 20%.
∴New ratio of salaries will be 4 × 1.1 :5 × 1.2
= 11 : 15.
Increase of 10% and 20%.
∴New ratio of salaries will be 4 × 1.1 :5 × 1.2
= 11 : 15.
Rae and Reena have arranged the bricks horizontally one above the other. If the length, width and height of each brick are 6 inches, 3 inches, and 3 inches, respectively then how many rows of the bricks will be required to create a 3.5 meter wall?- a)46
- b)58
- c)42
- d)64
- e)32
Correct answer is option 'A'. Can you explain this answer?
Rae and Reena have arranged the bricks horizontally one above the other. If the length, width and height of each brick are 6 inches, 3 inches, and 3 inches, respectively then how many rows of the bricks will be required to create a 3.5 meter wall?
a)
46
b)
58
c)
42
d)
64
e)
32
|
|
Elite Coaching Classes answered |
Height of a brick = 3 inches
We know, 1 meter = 39.3701 inches ≈ 39.4 inches
Height of the wall = 3.5 meters = 3.5 × 39.4 = 137.9 inches
Total rows of bricks required to create the wall = 137.9/3 = 45.97 ≈ 46
∴ A total of 46 rows of bricks will be required to create a 3.5-meter wall.
The average weight of P and his three friends is 55 kg. If P is 4 kg more than the average weight of his three friends, what is P's weight (in kg)?- a)60
- b)54
- c)58
- d)62
- e)56
Correct answer is option 'C'. Can you explain this answer?
The average weight of P and his three friends is 55 kg. If P is 4 kg more than the average weight of his three friends, what is P's weight (in kg)?
a)
60
b)
54
c)
58
d)
62
e)
56
|
|
Elite Coaching Classes answered |
The total weight of P and his three friends = 55 × 4 = 220 kg
Let, the average weight of three friends = x
So, the total weight of three friends = 3x
The weight of P = x + 4
Then, (x + 4) + 3x = 220
⇒ 4x + 4 = 220
⇒ 4x = 220 - 4 = 216
⇒ x = 216/4 = 54
∴ P's weight = 4 + 54 = 58 kg
∴ The P's weight (in kg) is 58 kg
The average of nine numbers is 60, that of the first five numbers is 55 and the next three is 65. The ninth number is 10 less than the tenth number. Then, tenth number is –- a)80
- b)70
- c)75
- d)85
- e)72
Correct answer is option 'A'. Can you explain this answer?
The average of nine numbers is 60, that of the first five numbers is 55 and the next three is 65. The ninth number is 10 less than the tenth number. Then, tenth number is –
a)
80
b)
70
c)
75
d)
85
e)
72
|
|
Elite Coaching Classes answered |
The sum of nine numbers = 60 × 9 = 540
The sum of the first five numbers = 55 × 5 = 275
The sum of the next three numbers = 65 × 3 = 195
Ninth number = (540 – 275 – 195) = (540 – 470) = 70
∴ Tenth number = 70 + 10 = 80
Two mutually perpendicular chords AB and CD meet at a point P inside the circle such that AP = 6 cms, PB = 4 units and DP = 3 units. What is the area of the circle?- a)125π/4 sq cms
- b)100π/7 sq cms
- c)125π/8 sq cms
- d)52π/3 sq cms
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
Two mutually perpendicular chords AB and CD meet at a point P inside the circle such that AP = 6 cms, PB = 4 units and DP = 3 units. What is the area of the circle?
a)
125π/4 sq cms
b)
100π/7 sq cms
c)
125π/8 sq cms
d)
52π/3 sq cms
e)
None of these
|
|
Swati Sharma answered |
As AB and CD are two chords that intersect at O, AP x PB = CP x PD
6 x 4 = CP x 3
CP = 8
From center O draw OM ⊥r AB and ON ⊥r CD.
From the center a line ⊥r to a chord bisects the chord.
So, we have AM = MB = 5 cm
MP = 1 cm, ON = 1 cm, CD = 11 cm, CN = 5.5 cm
ON2 + CN2 = OC2
12 + 5.52 + r2
1 + 30.25 = r2
Area = πr2
π x 31.25
31.25π = 125π/4 sq cms
6 x 4 = CP x 3
CP = 8
From center O draw OM ⊥r AB and ON ⊥r CD.
From the center a line ⊥r to a chord bisects the chord.
So, we have AM = MB = 5 cm
MP = 1 cm, ON = 1 cm, CD = 11 cm, CN = 5.5 cm
ON2 + CN2 = OC2
12 + 5.52 + r2
1 + 30.25 = r2
Area = πr2
π x 31.25
31.25π = 125π/4 sq cms
The question is "What is the area of the circle?"
Hence, the answer is 125π/4 sq cms.
Choice A is the correct answer.
A solid cube of side 8 cm is dropped into a rectangular container of length 16 cm, breadth 8 cm and height 15 cm which is partly filled with water. If the cube is completely submerged, then the rise of water level (in cm) is:- a)6
- b)4
- c)2
- d)5
- e)3
Correct answer is option 'B'. Can you explain this answer?
A solid cube of side 8 cm is dropped into a rectangular container of length 16 cm, breadth 8 cm and height 15 cm which is partly filled with water. If the cube is completely submerged, then the rise of water level (in cm) is:
a)
6
b)
4
c)
2
d)
5
e)
3
|
|
Elite Coaching Classes answered |
The volume of cube = The volume of the rectangular container with a length of 16 cm, breadth of 8 cm, and height of the water level rise
Let, the height of the water level will rise = x cm
So, 83 = 16 × 8 × x
⇒ 512 = 128 × x
⇒ x = 512/128 = 4
∴ The rise of water level (in cm) is 4 cm
An inverted right circular cone has a radius of 9 cm. This cone is partly filled with oil which is dipping from a hole in the tip at a rate of 1cm2/hour. Currently the level of oil 3 cm from top and surface area is 36π cm2. How long will it take the cone to be completely empty?- a)72π hours
- b)1 hour
- c)3 hours
- d)36π hours
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
An inverted right circular cone has a radius of 9 cm. This cone is partly filled with oil which is dipping from a hole in the tip at a rate of 1cm2/hour. Currently the level of oil 3 cm from top and surface area is 36π cm2. How long will it take the cone to be completely empty?
a)
72π hours
b)
1 hour
c)
3 hours
d)
36π hours
e)
None of these
|
Harper Patel answered |
To find the height of the cone, we can use the formula for the volume of a cone:
V = (1/3)πr^2h
where V is the volume, r is the radius, and h is the height.
Since the cone is partly filled with oil up to a level 3 cm from the top, the height of the oil is the total height of the cone minus 3 cm.
So, h = total height - 3 cm
To find the total height, we can use the formula for the surface area of a cone:
A = πr(r + √(r^2 + h^2))
where A is the surface area.
Since the surface area is given as 36 cm^2, we can substitute the values into the equation:
36 = π(9)(9 + √(9^2 + h^2))
Now we can solve for h:
36/π = 81 + √(81 + h^2)
36/π - 81 = √(81 + h^2)
(36/π - 81)^2 = 81 + h^2
h^2 = (36/π - 81)^2 - 81
h = √((36/π - 81)^2 - 81)
Using a calculator, we find that h ≈ 6.81 cm.
Therefore, the height of the cone is approximately 6.81 cm.
V = (1/3)πr^2h
where V is the volume, r is the radius, and h is the height.
Since the cone is partly filled with oil up to a level 3 cm from the top, the height of the oil is the total height of the cone minus 3 cm.
So, h = total height - 3 cm
To find the total height, we can use the formula for the surface area of a cone:
A = πr(r + √(r^2 + h^2))
where A is the surface area.
Since the surface area is given as 36 cm^2, we can substitute the values into the equation:
36 = π(9)(9 + √(9^2 + h^2))
Now we can solve for h:
36/π = 81 + √(81 + h^2)
36/π - 81 = √(81 + h^2)
(36/π - 81)^2 = 81 + h^2
h^2 = (36/π - 81)^2 - 81
h = √((36/π - 81)^2 - 81)
Using a calculator, we find that h ≈ 6.81 cm.
Therefore, the height of the cone is approximately 6.81 cm.
A drum contains 263L 520 mL of oil. This oil is filled into 45 containers each of equal size. How much oil is there in 25 such containers?- a)144.6 L
- b)146.4 L
- c)142.8 L
- d)150.5 L
- e)143.2 L
Correct answer is option 'B'. Can you explain this answer?
A drum contains 263L 520 mL of oil. This oil is filled into 45 containers each of equal size. How much oil is there in 25 such containers?
a)
144.6 L
b)
146.4 L
c)
142.8 L
d)
150.5 L
e)
143.2 L
|
|
Sophia Baker answered |
To find the amount of oil in 25 containers, we first need to determine the amount of oil in one container.
Given that the drum contains 263L 520 mL of oil and it is filled into 45 containers of equal size, we can calculate the amount of oil in one container by dividing the total amount of oil by the number of containers.
263L 520 mL ÷ 45 = 5857 mL
Therefore, each container contains 5857 mL of oil.
To find the amount of oil in 25 containers, we multiply the amount of oil in one container by the number of containers.
5857 mL × 25 = 146,425 mL
However, the answer choices are given in liters, so we need to convert milliliters to liters.
146,425 mL ÷ 1000 = 146.425 L
Therefore, there is 146.425 liters of oil in 25 containers.
The correct answer is option B) 146.4 L.
Given that the drum contains 263L 520 mL of oil and it is filled into 45 containers of equal size, we can calculate the amount of oil in one container by dividing the total amount of oil by the number of containers.
263L 520 mL ÷ 45 = 5857 mL
Therefore, each container contains 5857 mL of oil.
To find the amount of oil in 25 containers, we multiply the amount of oil in one container by the number of containers.
5857 mL × 25 = 146,425 mL
However, the answer choices are given in liters, so we need to convert milliliters to liters.
146,425 mL ÷ 1000 = 146.425 L
Therefore, there is 146.425 liters of oil in 25 containers.
The correct answer is option B) 146.4 L.
Find the ratio of the diagonal of a square of side 30 cm, to its side.- a)√2: 3
- b)√3: 4
- c)1 : √2
- d)√2: 1
- e)√3: 1
Correct answer is option 'D'. Can you explain this answer?
Find the ratio of the diagonal of a square of side 30 cm, to its side.
a)
√2: 3
b)
√3: 4
c)
1 : √2
d)
√2: 1
e)
√3: 1
|
|
Elite Coaching Classes answered |
Diagonal of a square = √2 side.
Hence this is the required ratio. So the required ratio is √2: 1.
Hence this is the required ratio. So the required ratio is √2: 1.
A wire is bent to form a square of side 22 cm. If the wire is rebent to form a circle, then its radius will be: - a)22 cm
- b)14 cm
- c)11 cm
- d)7 cm
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
A wire is bent to form a square of side 22 cm. If the wire is rebent to form a circle, then its radius will be:
a)
22 cm
b)
14 cm
c)
11 cm
d)
7 cm
e)
None of these
|
|
Swati Sharma answered |
Let us assume the radius of the circle be r
⇒ The perimeter of the square = 4 × 22 = 88 cm
⇒ The circumference of the circle = 2 × π × r
⇒ 88 = 2 × (22/7) × r
⇒ r = 88 × 7 / 22 × 2
⇒ r = 14 cm
∴ The required result will be 14 cm.
A circular pond has an area equal to 616 m2. A circular stage is made at the centre of the pond whose radius is equal to half the radius of the pond. What is the area where water is present?- a)454 sq. m
- b)462 sq. m
- c)532 sq. m
- d)564 sq. M
- e)Not Attempted
Correct answer is option 'B'. Can you explain this answer?
A circular pond has an area equal to 616 m2. A circular stage is made at the centre of the pond whose radius is equal to half the radius of the pond. What is the area where water is present?
a)
454 sq. m
b)
462 sq. m
c)
532 sq. m
d)
564 sq. M
e)
Not Attempted
|
|
Swati Sharma answered |
Let the radius of the pond be R metres.
Then, πR2 = 616 → R2 = 616 × 7 / 22 = 196 → R = 14 m.
Radius of the stage = (14 / 2) m = 7 m.
Area where water is present
= π (142 - 72) = (22/7 × 21×7) m2
= 462 m2.
= 462 m2.
A sum of money at simple interest amounts to Rs. 815 in 3 years and Rs. 854 in 4 years. The sum is- a)Rs. 650
- b)Rs. 690
- c)Rs. 698
- d)Rs. 700
- e)Rs. 680
Correct answer is option 'C'. Can you explain this answer?
A sum of money at simple interest amounts to Rs. 815 in 3 years and Rs. 854 in 4 years. The sum is
a)
Rs. 650
b)
Rs. 690
c)
Rs. 698
d)
Rs. 700
e)
Rs. 680
|
|
Swati Sharma answered |
Simple Interest for 1 year = Rs. (854 − 815)
= Rs. 39
Simple Interest for 3 years = Rs. 39 × 3
⇒ Rs. 117
Principal = Rs. 815 − Rs. 117
⇒ Rs. 698
∴ The sum is Rs. 698.
A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?- a)8.2
- b)4.2
- c)6.1
- d)7.2
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
a)
8.2
b)
4.2
c)
6.1
d)
7.2
e)
None of these
|
|
Swati Sharma answered |
It is given in the question that a man crosses 600m long street in 5 minutes. We have to find the speed of the man in km per hour. To find the speed of the man in km per hour, we have to convert the given distance to km and also convert the given time to hour.
First, let us see the conversion of the given distance into km. We know that 1km = 1000m.
So, to convert 600m to km, we can write, 600m = x km.
x = 600/1000 km
x = 0.6km
Now, let us convert the given time into hours. We know that 1 hour = 60 minutes.
So, to convert 5 minutes to hours, we can write, 5 minutes = y hours.
y = 5/60 hrs
y = 0.083 hrs
Now we know that speed can be found out using the formula, Speed=Distance/Time, We have found out that distance = 0.6km and time = 0.083 hrs. So, on substituting these values in the formula of speed, we get,
Speed = 0.6/ 0.083
= 6 × 1000 / 83 × 10
= 6000/ 830
= 600/83
= 7.2 km/h
Therefore, we get the speed of the man crossing a 600m long street in 5 minutes as 7.2km/h.
Hence, option (D) is the correct answer.
First, let us see the conversion of the given distance into km. We know that 1km = 1000m.
So, to convert 600m to km, we can write, 600m = x km.
x = 600/1000 km
x = 0.6km
Now, let us convert the given time into hours. We know that 1 hour = 60 minutes.
So, to convert 5 minutes to hours, we can write, 5 minutes = y hours.
y = 5/60 hrs
y = 0.083 hrs
Now we know that speed can be found out using the formula, Speed=Distance/Time, We have found out that distance = 0.6km and time = 0.083 hrs. So, on substituting these values in the formula of speed, we get,
Speed = 0.6/ 0.083
= 6 × 1000 / 83 × 10
= 6000/ 830
= 600/83
= 7.2 km/h
Therefore, we get the speed of the man crossing a 600m long street in 5 minutes as 7.2km/h.
Hence, option (D) is the correct answer.
Rs.750 are divided among A, B and C in such a manner that A : B is 5 : 2 and B : C is 7 : 13. What is A’s share?- a)Rs.140
- b)Rs. 350
- c)Rs. 250
- d)Rs. 260
- e)Rs.280
Correct answer is option 'B'. Can you explain this answer?
Rs.750 are divided among A, B and C in such a manner that A : B is 5 : 2 and B : C is 7 : 13. What is A’s share?
a)
Rs.140
b)
Rs. 350
c)
Rs. 250
d)
Rs. 260
e)
Rs.280
|
|
Swati Sharma answered |
A : B = 5 : 2
B : C = 7 : 13
A : B : C = 5 × 7 : 2 × 7 : 2 × 13 = 35 : 14 : 26
Total Sum = 750
⇒ 35 x + 14x + 26x = 750
⇒ x = 10
So, A's share = 35 × 10 = Rs 350
∴ The required answer is Rs 350
u : v = 4 : 7 and v : w = 9 : 7. If u = 72, then what is the value of w?- a)98
- b)77
- c)63
- d)49
- e)56
Correct answer is option 'A'. Can you explain this answer?
u : v = 4 : 7 and v : w = 9 : 7. If u = 72, then what is the value of w?
a)
98
b)
77
c)
63
d)
49
e)
56
|
|
Swati Sharma answered |
u : v = 4 : 7 and v : w = 9 : 7
To make ratio v equal in both cases
We have to multiply the 1st ratio by 9 and 2nd ratio by 7
u : v = 9 × 4 : 9 × 7 = 36 : 63 ----(i)
v : w = 9 × 7 : 7 × 7 = 63 : 49 ----(ii)
Form (i) and (ii), we can see that the ratio v is equal in both cases
So, Equating the ratios we get,
u ∶ v ∶ w = 36 ∶ 63 ∶ 49
⇒ u ∶ w = 36 ∶ 49
When u = 72,
⇒ w = 49 × 72/36 = 98
∴ Value of w is 98
The price of an article is increased by 16 (2/3)%. By what percentage the customer should reduce his consumption such the expenditure is increased by only 12%?- a)5%
- b)6%
- c)7%
- d)4%
- e)Not Attempted
Correct answer is option 'D'. Can you explain this answer?
The price of an article is increased by 16 (2/3)%. By what percentage the customer should reduce his consumption such the expenditure is increased by only 12%?
a)
5%
b)
6%
c)
7%
d)
4%
e)
Not Attempted
|
|
Elite Coaching Classes answered |
We know that
Product of price and consumption is equal to the expenditure
Let the original price of article be x units
According to the question,
Price is increased by 24%
New price of article = x + 16(2/3)% of x = 7x/6
Let the original consumption be y
Original expenditure = xy
Expenditure is increased by 12%
New expenditure = xy + (12/100) × xy = 28xy/25
New consumption = (New expenditure)/(New Price)
New consumption = (28xy/25)/(7x/6) = 24y/25
Decrease in consumption = (y) – (24y/25) = y/25
Required percentage = (y/25)/y × 100 = 4%
The average monthly salary of 12 workers and 3 managers in a factory was Rs. 600. When one of the managers whose salary was Rs. 720, was replaced with a new manager, the average salary of the team went down to Rs. 580. What is the salary of the new manager?- a)Rs. 570
- b)Rs. 420
- c)Rs. 690
- d)Rs. 640
- e)Rs. 610
Correct answer is option 'B'. Can you explain this answer?
The average monthly salary of 12 workers and 3 managers in a factory was Rs. 600. When one of the managers whose salary was Rs. 720, was replaced with a new manager, the average salary of the team went down to Rs. 580. What is the salary of the new manager?
a)
Rs. 570
b)
Rs. 420
c)
Rs. 690
d)
Rs. 640
e)
Rs. 610
|
|
Elite Coaching Classes answered |
Initially, the average monthly salary of 12 workers and 3 managers was Rs. 600. This means the total salary for all 12 workers and 3 managers combined was 15 * Rs. 600 = Rs. 9,000.
One of the managers had a salary of Rs. 720. This means the total salary for the remaining 11 workers and 2 managers was Rs. 9,000 - Rs. 720 = Rs. 8,280.
Now, we are told that when the new manager replaces the previous manager, the average salary of the team drops to Rs. 580. We can set up the equation:
(8,280 + x) / 15 = 580
Here, 'x' represents the salary of the new manager. We need to solve this equation to find the value of 'x'.
To solve the equation, we first multiply both sides by 15:
8,280 + x = 580 * 15
8,280 + x = 8,700
8,280 + x = 8,700
Next, subtract 8,280 from both sides:
x = 8,700 - 8,280
x = 420
x = 420
Therefore, the salary of the new manager is Rs. 420.
The correct answer is (b) Rs. 420.
Anu brought 2 kg 500 g Laddu, 3 kg 250 g Jalebi and 4 kg Rasgullas from a sweet shop. The shopkeeper packed everything together in boxes with a maximum capacity of 750 g. How many boxes required to pack all the items?- a)15
- b)13
- c)14
- d)12
- e)11
Correct answer is option 'B'. Can you explain this answer?
Anu brought 2 kg 500 g Laddu, 3 kg 250 g Jalebi and 4 kg Rasgullas from a sweet shop. The shopkeeper packed everything together in boxes with a maximum capacity of 750 g. How many boxes required to pack all the items?
a)
15
b)
13
c)
14
d)
12
e)
11
|
|
Swati Sharma answered |
Total amount of Laddu = 2 kg 500 g = (2 × 1000) + 500 = 2500 g
Total amount of Jalebi = 3 kg 250 g = (3 × 1000) + 250 = 3250 g
Total amount of Rasgulla = 4 kg = (4 × 1000) = 4000 g
Total amount = (2500 + 3250 + 4000) = 9750 g
Maximum capacity of a box = 750 g
Total box required = 9750/750 = 13
∴ Total 13 boxes required to pack all the items.
A car travels some distance at a speed of 8 km/hr and returns at a speed of 12 km/hr. If the total time taken by the car is 15 hours, then what is the distance (in km)?- a)48
- b)60
- c)56
- d)72
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
A car travels some distance at a speed of 8 km/hr and returns at a speed of 12 km/hr. If the total time taken by the car is 15 hours, then what is the distance (in km)?
a)
48
b)
60
c)
56
d)
72
e)
None of these
|
|
Elite Coaching Classes answered |
Let the distance be d km.
We know that,
Distance = Speed x Time
⇒ d = 72 km
Running at a speed of 60 km per hour, a train passed through a 1.5 km long tunnel in two minutes, What is the length of the train ?- a)250 m
- b)500 m
- c)1000 m
- d)1500 m
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
Running at a speed of 60 km per hour, a train passed through a 1.5 km long tunnel in two minutes, What is the length of the train ?
a)
250 m
b)
500 m
c)
1000 m
d)
1500 m
e)
None of these
|
|
Elite Coaching Classes answered |
Let the length of the train be L
According to the question,
Total distance = 1500 m + L
Speed = 60(5/18)
⇒ 50/3 m/sec
Time = 2 × 60 = 120 sec
⇒ 1500 + L = (50/3)× 120
⇒ L = 2000 - 1500
⇒ L = 500 m
∴ The length of the train is 500 m.
Chapter doubts & questions for Quantitative Reasoning - Topic-wise Practice Tests for UCAT 2025 is part of UCAT exam preparation. The chapters have been prepared according to the UCAT exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for UCAT 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
Chapter doubts & questions of Quantitative Reasoning - Topic-wise Practice Tests for UCAT in English & Hindi are available as part of UCAT exam.
Download more important topics, notes, lectures and mock test series for UCAT Exam by signing up for free.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup