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A and B complete a work in 6 days. A alone can do it in 10 days. then B alone will do it in how many days?
- a)15 days
- b)8 days
- c)12 days
- d)14 days
Correct answer is option 'A'. Can you explain this answer?
A and B complete a work in 6 days. A alone can do it in 10 days. then B alone will do it in how many days?
a)
15 days
b)
8 days
c)
12 days
d)
14 days
|
Codebreakers answered |
Given:
Time taken by A and B = 6 days
Time taken by A = 10 days
Formula used:
Total work = Time taken × Efficiency
Calculation:
L.C.M of (6 and 10) = 30 = Total work
Efficiency of A and B = 30/6 = 5 units/day
Efficiency of B = 30/10 = 3 units/day
Efficiency of B = (5 – 3) units/day
⇒ 2 units/day
Time taken by B = 30/2 days
⇒ 15 days
∴ B will complete the work in 15 days
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A car covers a distance of 624 km in 6 ½ hours. Find its speed?
- a)96 km/hr
- b)140 km/hr
- c)104 km/hr
- d)10.4 km/hr
Correct answer is option 'A'. Can you explain this answer?
A car covers a distance of 624 km in 6 ½ hours. Find its speed?
a)
96 km/hr
b)
140 km/hr
c)
104 km/hr
d)
10.4 km/hr
|
|
Codebreakers answered |
Here the distance is 624km and the time taken is 6 1/2 hours which can be written as 6.5 hours. So, Speed = 624/ 6.5 = 96 km/hr. Car's speed is 96 km/hr.
A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?- a)15 days
- b) 14 days
- c)13 days
- d) 11 days
Correct answer is option 'D'. Can you explain this answer?
A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?
a)
15 days
b)
14 days
c)
13 days
d)
11 days
|
Saranya Gupta answered |
Calculation:
Step 1: Find the combined work rate of A, B, and C
Given:
A takes 24 days to complete the work, so A's work rate = 1/24
B takes 30 days to complete the work, so B's work rate = 1/30
C takes 40 days to complete the work, so C's work rate = 1/40
Combined work rate of A, B, and C = 1/24 + 1/30 + 1/40
= 5/120 + 4/120 + 3/120
= 12/120
= 1/10
Therefore, A, B, and C together can complete 1/10 of the work in 1 day.
Step 2: Calculate the total number of days taken to complete the work
Let the total number of days taken to complete the work be x days.
Since A, B, and C together can complete 1/10 of the work in 1 day, in x days, they can complete x/10 of the work.
Given that C leaves 4 days before the completion of the work, the remaining work is 1 - x/10 = (10 - x)/10
Since A and B are still working together, their combined work rate is 1/24 + 1/30 = 7/120
Therefore, (10 - x)/10 = (7/120) * (x-4)
Solving the above equation:
(10 - x)/10 = (7/120) * (x-4)
120(10 - x) = 7(x-4) * 10
1200 - 120x = 70x - 280
1200 + 280 = 70x + 120x
1480 = 190x
x = 1480/190
x = 7.79
Therefore, the work is done in approximately 8 days, which is closest to 11 days (option D).
Step 1: Find the combined work rate of A, B, and C
Given:
A takes 24 days to complete the work, so A's work rate = 1/24
B takes 30 days to complete the work, so B's work rate = 1/30
C takes 40 days to complete the work, so C's work rate = 1/40
Combined work rate of A, B, and C = 1/24 + 1/30 + 1/40
= 5/120 + 4/120 + 3/120
= 12/120
= 1/10
Therefore, A, B, and C together can complete 1/10 of the work in 1 day.
Step 2: Calculate the total number of days taken to complete the work
Let the total number of days taken to complete the work be x days.
Since A, B, and C together can complete 1/10 of the work in 1 day, in x days, they can complete x/10 of the work.
Given that C leaves 4 days before the completion of the work, the remaining work is 1 - x/10 = (10 - x)/10
Since A and B are still working together, their combined work rate is 1/24 + 1/30 = 7/120
Therefore, (10 - x)/10 = (7/120) * (x-4)
Solving the above equation:
(10 - x)/10 = (7/120) * (x-4)
120(10 - x) = 7(x-4) * 10
1200 - 120x = 70x - 280
1200 + 280 = 70x + 120x
1480 = 190x
x = 1480/190
x = 7.79
Therefore, the work is done in approximately 8 days, which is closest to 11 days (option D).
A and B can finish a work in 16 days while A alone can do the same work in 24 days. In how many days B alone will complete the work?- a)56
- b)48
- c)36
- d)58
Correct answer is option 'B'. Can you explain this answer?
A and B can finish a work in 16 days while A alone can do the same work in 24 days. In how many days B alone will complete the work?
a)
56
b)
48
c)
36
d)
58
|
Meera Menon answered |
Solution:
First, let's determine the work done by A and B together in one day:
A and B together can finish the work in 16 days, so their combined work rate per day is 1/16.
Work rate of A + Work rate of B = Combined work rate
Let the work rate of A be x and work rate of B be y.
x + y = 1/16
Given that A alone can complete the work in 24 days:
A's work rate = 1/24
Now, we can write the equation for A's work rate:
x = 1/24
We can substitute x = 1/24 into the first equation to find the work rate of B:
1/24 + y = 1/16
y = 1/16 - 1/24
y = 3/48 - 2/48
y = 1/48
Therefore, B's work rate is 1/48, which means B alone can complete the work in 48 days.
So, the correct answer is option B) 48.
First, let's determine the work done by A and B together in one day:
A and B together can finish the work in 16 days, so their combined work rate per day is 1/16.
Work rate of A + Work rate of B = Combined work rate
Let the work rate of A be x and work rate of B be y.
x + y = 1/16
Given that A alone can complete the work in 24 days:
A's work rate = 1/24
Now, we can write the equation for A's work rate:
x = 1/24
We can substitute x = 1/24 into the first equation to find the work rate of B:
1/24 + y = 1/16
y = 1/16 - 1/24
y = 3/48 - 2/48
y = 1/48
Therefore, B's work rate is 1/48, which means B alone can complete the work in 48 days.
So, the correct answer is option B) 48.
Express 25 mps in kmph?- a)15 kmph
- b)99 kmph
- c)90 kmph
- d)None
Correct answer is option 'C'. Can you explain this answer?
Express 25 mps in kmph?
a)
15 kmph
b)
99 kmph
c)
90 kmph
d)
None
|
Anushka Patel answered |
Converting 25 mps to kmph:
To convert meters per second (mps) to kilometers per hour (kmph), you need to remember that 1 meter per second is equal to 3.6 kilometers per hour.
Calculation:
- Given speed: 25 mps
- Conversion factor: 3.6 kmph
Using the formula:
Speed in kmph = Speed in mps * 3.6
Speed in kmph = 25 * 3.6
Speed in kmph = 90 kmph
Therefore, the speed of 25 meters per second is equivalent to 90 kilometers per hour. Hence, the correct answer is option 'C' - 90 kmph.
To convert meters per second (mps) to kilometers per hour (kmph), you need to remember that 1 meter per second is equal to 3.6 kilometers per hour.
Calculation:
- Given speed: 25 mps
- Conversion factor: 3.6 kmph
Using the formula:
Speed in kmph = Speed in mps * 3.6
Speed in kmph = 25 * 3.6
Speed in kmph = 90 kmph
Therefore, the speed of 25 meters per second is equivalent to 90 kilometers per hour. Hence, the correct answer is option 'C' - 90 kmph.
The radius of a circle is increased by 1%. Find how much % does its area increases?- a)1.01%
- b) 5.01%
- c)3.01%
- d)2.01%
Correct answer is option 'D'. Can you explain this answer?
The radius of a circle is increased by 1%. Find how much % does its area increases?
a)
1.01%
b)
5.01%
c)
3.01%
d)
2.01%
|
Prateek Dasgupta answered |
Understanding the Problem
When the radius of a circle is increased by 1%, we need to determine the percentage increase in the area of the circle.
Area of a Circle
- The formula for the area (A) of a circle is given by:
A = πr², where r is the radius.
Calculating the New Radius
- If the original radius is r, after a 1% increase, the new radius (r') can be calculated as:
r' = r + 0.01r = 1.01r.
Calculating the New Area
- The new area (A') with the new radius can be found using:
A' = π(r')² = π(1.01r)² = π(1.0201r²).
Finding the Percentage Increase in Area
- The original area (A) is:
A = πr².
- The new area (A') becomes:
A' = π(1.0201r²) = 1.0201A.
- To find the percentage increase in the area:
Percentage Increase = [(A' - A) / A] × 100
= [(1.0201A - A) / A] × 100
= (0.0201) × 100 ≈ 2.01%.
Conclusion
- Therefore, the area of the circle increases by approximately 2.01% when the radius is increased by 1%.
- The correct answer is option 'D'.
When the radius of a circle is increased by 1%, we need to determine the percentage increase in the area of the circle.
Area of a Circle
- The formula for the area (A) of a circle is given by:
A = πr², where r is the radius.
Calculating the New Radius
- If the original radius is r, after a 1% increase, the new radius (r') can be calculated as:
r' = r + 0.01r = 1.01r.
Calculating the New Area
- The new area (A') with the new radius can be found using:
A' = π(r')² = π(1.01r)² = π(1.0201r²).
Finding the Percentage Increase in Area
- The original area (A) is:
A = πr².
- The new area (A') becomes:
A' = π(1.0201r²) = 1.0201A.
- To find the percentage increase in the area:
Percentage Increase = [(A' - A) / A] × 100
= [(1.0201A - A) / A] × 100
= (0.0201) × 100 ≈ 2.01%.
Conclusion
- Therefore, the area of the circle increases by approximately 2.01% when the radius is increased by 1%.
- The correct answer is option 'D'.
A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?- a)Rs.18000
- b)Rs.15000
- c)Rs.17000
- d)Rs.14000
Correct answer is option 'D'. Can you explain this answer?
A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
a)
Rs.18000
b)
Rs.15000
c)
Rs.17000
d)
Rs.14000
|
Vaishnavi Bose answered |
Calculation of C's share in the annual profit:
Step 1: Calculate the ratio of investments
- A's investment = Rs. 25000 for 12 months
- B's investment = Rs. 30000 for 12 months
- C's investment = Rs. 35000 for 8 months (since C joined after 4 months)
Total investment = Rs. 25000 x 12 + Rs. 30000 x 12 + Rs. 35000 x 8
= Rs. 300000 + Rs. 360000 + Rs. 280000
= Rs. 940000
Ratio of investments:
A : B : C = 25000 x 12 : 30000 x 12 : 35000 x 8
= 300000 : 360000 : 280000
= 15 : 18 : 14
Step 2: Calculate C's share in the annual profit
C's share = (C's investment / Total investment) x Total profit
= (14/47) x Rs. 47000
= Rs. 14000
Therefore, C's share in the annual profit of Rs. 47000 is Rs. 14000. The correct answer is option 'D'.
Step 1: Calculate the ratio of investments
- A's investment = Rs. 25000 for 12 months
- B's investment = Rs. 30000 for 12 months
- C's investment = Rs. 35000 for 8 months (since C joined after 4 months)
Total investment = Rs. 25000 x 12 + Rs. 30000 x 12 + Rs. 35000 x 8
= Rs. 300000 + Rs. 360000 + Rs. 280000
= Rs. 940000
Ratio of investments:
A : B : C = 25000 x 12 : 30000 x 12 : 35000 x 8
= 300000 : 360000 : 280000
= 15 : 18 : 14
Step 2: Calculate C's share in the annual profit
C's share = (C's investment / Total investment) x Total profit
= (14/47) x Rs. 47000
= Rs. 14000
Therefore, C's share in the annual profit of Rs. 47000 is Rs. 14000. The correct answer is option 'D'.
5 men and 12 boys finish a piece of work in 4 days, 7 men and 6 boys do it in 5 days. The ratio between the efficiencies of a man and boy is?- a)1:2
- b)2:1
- c)2:3
- d)6:5
Correct answer is option 'D'. Can you explain this answer?
5 men and 12 boys finish a piece of work in 4 days, 7 men and 6 boys do it in 5 days. The ratio between the efficiencies of a man and boy is?
a)
1:2
b)
2:1
c)
2:3
d)
6:5
|
|
Bhaskar Datta answered |
Understanding the Problem
To find the ratio of efficiencies between a man and a boy, we first need to establish the equations based on the given information.
Work Done by Men and Boys
1. **First Equation (5 Men and 12 Boys)**:
- Work done in 4 days can be expressed as:
- \(5m + 12b = \frac{W}{4}\), where \(m\) is the efficiency of a man, \(b\) is the efficiency of a boy, and \(W\) is the total work.
2. **Second Equation (7 Men and 6 Boys)**:
- Work done in 5 days can be expressed as:
- \(7m + 6b = \frac{W}{5}\).
Setting Up the Equations
From the above two equations, we have:
- From the first equation:
- \(20m + 48b = W\) (by multiplying the entire equation by 4).
- From the second equation:
- \(35m + 30b = W\) (by multiplying the entire equation by 5).
Equating the Work
Now, we can set the two equations equal to each other:
- \(20m + 48b = 35m + 30b\)
Simplifying the Equation
Rearranging gives us:
- \(20m - 35m = 30b - 48b\)
- \(-15m = -18b\)
- Thus, \(15m = 18b\) or \(\frac{m}{b} = \frac{18}{15} = \frac{6}{5}\).
Conclusion
The ratio between the efficiencies of a man and a boy is:
- \(m:b = 6:5\).
Thus, the correct answer is option 'D'.
To find the ratio of efficiencies between a man and a boy, we first need to establish the equations based on the given information.
Work Done by Men and Boys
1. **First Equation (5 Men and 12 Boys)**:
- Work done in 4 days can be expressed as:
- \(5m + 12b = \frac{W}{4}\), where \(m\) is the efficiency of a man, \(b\) is the efficiency of a boy, and \(W\) is the total work.
2. **Second Equation (7 Men and 6 Boys)**:
- Work done in 5 days can be expressed as:
- \(7m + 6b = \frac{W}{5}\).
Setting Up the Equations
From the above two equations, we have:
- From the first equation:
- \(20m + 48b = W\) (by multiplying the entire equation by 4).
- From the second equation:
- \(35m + 30b = W\) (by multiplying the entire equation by 5).
Equating the Work
Now, we can set the two equations equal to each other:
- \(20m + 48b = 35m + 30b\)
Simplifying the Equation
Rearranging gives us:
- \(20m - 35m = 30b - 48b\)
- \(-15m = -18b\)
- Thus, \(15m = 18b\) or \(\frac{m}{b} = \frac{18}{15} = \frac{6}{5}\).
Conclusion
The ratio between the efficiencies of a man and a boy is:
- \(m:b = 6:5\).
Thus, the correct answer is option 'D'.
Express a speed of 36 kmph in meters per second?- a)10 mps
- b)12 mps
- c)14 mps
- d)17 mps
Correct answer is option 'A'. Can you explain this answer?
Express a speed of 36 kmph in meters per second?
a)
10 mps
b)
12 mps
c)
14 mps
d)
17 mps
|
|
Prasenjit Verma answered |
Converting 36 kmph to meters per second
To convert kilometers per hour (kmph) to meters per second (mps), we need to use the following conversion factor:
1 kmph = 1000 meters / 3600 seconds = 5/18 mps
Calculating the speed
Given speed = 36 kmph
To convert this to meters per second, we multiply by the conversion factor:
Speed in mps = 36 kmph * 5/18 mps
Speed in mps = 10 mps
Therefore, the speed of 36 kmph is equivalent to 10 meters per second. Hence, option 'A' is the correct answer.
To convert kilometers per hour (kmph) to meters per second (mps), we need to use the following conversion factor:
1 kmph = 1000 meters / 3600 seconds = 5/18 mps
Calculating the speed
Given speed = 36 kmph
To convert this to meters per second, we multiply by the conversion factor:
Speed in mps = 36 kmph * 5/18 mps
Speed in mps = 10 mps
Therefore, the speed of 36 kmph is equivalent to 10 meters per second. Hence, option 'A' is the correct answer.
The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?- a)15 kmph
- b)12 kmph
- c)10 kmph
- d)5 kmph
Correct answer is option 'A'. Can you explain this answer?
The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
a)
15 kmph
b)
12 kmph
c)
10 kmph
d)
5 kmph
|
Nidhi Pillai answered |
Understanding the Problem
To solve the problem, we need to determine the distance covered by a train traveling at a speed of 90 kilometers per hour (kmph) over a time period of 10 minutes.
Conversion of Time
- The first step is to convert the time from minutes to hours, since the speed is given in kilometers per hour.
- 10 minutes is equivalent to:
Calculating Distance
- The formula to calculate distance is:
- Substituting the known values:
Conclusion
- Therefore, the distance covered by the train in 10 minutes is:
The correct answer is option 'A', which is 15 km.
To solve the problem, we need to determine the distance covered by a train traveling at a speed of 90 kilometers per hour (kmph) over a time period of 10 minutes.
Conversion of Time
- The first step is to convert the time from minutes to hours, since the speed is given in kilometers per hour.
- 10 minutes is equivalent to:
- 10 minutes ÷ 60 minutes/hour = 1/6 hours
Calculating Distance
- The formula to calculate distance is:
- Distance = Speed × Time
- Substituting the known values:
- Distance = 90 kmph × (1/6) hours
- Distance = 90/6 km = 15 km
Conclusion
- Therefore, the distance covered by the train in 10 minutes is:
- 15 kilometers
The correct answer is option 'A', which is 15 km.
A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?- a)10 days
- b)20 days
- c)5 days
- d)4 days
Correct answer is option 'B'. Can you explain this answer?
A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
a)
10 days
b)
20 days
c)
5 days
d)
4 days
|
|
Dhruba Datta answered |
Understanding the Problem
To determine how many days C can complete the work alone, we first need to calculate the work rates of A, B, and C.
Work Rates of A and B
- A can complete the work in 4 days, so A's work rate is 1/4 of the work per day.
- B can complete the work in 5 days, so B's work rate is 1/5 of the work per day.
Combined Work Rate of A and B
- The combined work rate of A and B is:
- (1/4) + (1/5) = 5/20 + 4/20 = 9/20
This means A and B together can complete 9/20 of the work in one day.
Work Completed with C's Assistance
- Together, A, B, and C completed the work in 2 days. Thus, their combined work rate is:
- 1 total work / 2 days = 1/2 of the work per day.
Finding C's Work Rate
- Since A and B together do 9/20 of the work in a day, we set up the equation:
- (Work rate of A + Work rate of B + Work rate of C) = 1/2
- (9/20 + Work rate of C) = 1/2
To find C's work rate, we convert 1/2 to a common denominator:
- 1/2 = 10/20
Now we can solve for C's work rate:
- 9/20 + Work rate of C = 10/20
- Work rate of C = 10/20 - 9/20 = 1/20
Calculating C's Time to Complete the Work Alone
- If C's work rate is 1/20 of the work per day, C can complete the entire work alone in:
- 1 / (1/20) = 20 days.
Thus, the answer is that C alone can do the work in 20 days.
Correct Answer
- The correct option is (b) 20 days.
To determine how many days C can complete the work alone, we first need to calculate the work rates of A, B, and C.
Work Rates of A and B
- A can complete the work in 4 days, so A's work rate is 1/4 of the work per day.
- B can complete the work in 5 days, so B's work rate is 1/5 of the work per day.
Combined Work Rate of A and B
- The combined work rate of A and B is:
- (1/4) + (1/5) = 5/20 + 4/20 = 9/20
This means A and B together can complete 9/20 of the work in one day.
Work Completed with C's Assistance
- Together, A, B, and C completed the work in 2 days. Thus, their combined work rate is:
- 1 total work / 2 days = 1/2 of the work per day.
Finding C's Work Rate
- Since A and B together do 9/20 of the work in a day, we set up the equation:
- (Work rate of A + Work rate of B + Work rate of C) = 1/2
- (9/20 + Work rate of C) = 1/2
To find C's work rate, we convert 1/2 to a common denominator:
- 1/2 = 10/20
Now we can solve for C's work rate:
- 9/20 + Work rate of C = 10/20
- Work rate of C = 10/20 - 9/20 = 1/20
Calculating C's Time to Complete the Work Alone
- If C's work rate is 1/20 of the work per day, C can complete the entire work alone in:
- 1 / (1/20) = 20 days.
Thus, the answer is that C alone can do the work in 20 days.
Correct Answer
- The correct option is (b) 20 days.
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