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Ajit, Rajat and Abhay can do a piece of work in 10, 12 and 15 days respectively. Ajit works for two days and then Rajat joins him. They together work for some days and then leave. Abhay completes the remaining work. If work gets completed in 35/4 days and they get ₹ 5000 for the work, find the share of Abhay in the money.
- a)1250
- b)1500
- c)1000
- d)1200
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Ajit, Rajat and Abhay can do a piece of work in 10, 12 and 15 days re...
Given information:
- Ajit can do the work in 10 days.
- Rajat can do the work in 12 days.
- Abhay can do the work in 15 days.
- Ajit works for 2 days.
- Then Rajat joins and they work together for some days.
- Finally, Abhay completes the remaining work.
- The total time taken to complete the work is 35/4 days.
- They get ₹5000 for the work.
Let's solve the problem step by step.
Step 1: Calculate the efficiency of each person
Efficiency is defined as the amount of work done in one day.
- Ajit's efficiency = 1/10 (as he can complete the work in 10 days)
- Rajat's efficiency = 1/12 (as he can complete the work in 12 days)
- Abhay's efficiency = 1/15 (as he can complete the work in 15 days)
Step 2: Find the work done by Ajit in 2 days
Ajit's efficiency = 1/10
Therefore, work done by Ajit in 2 days = (1/10) * 2 = 1/5
Step 3: Find the work done by Ajit and Rajat together
Ajit and Rajat work together for some days and complete a certain amount of work. Let's assume they work together for 'x' days.
Ajit's efficiency = 1/10
Rajat's efficiency = 1/12
Their combined efficiency = 1/10 + 1/12 = 6/60 + 5/60 = 11/60
Therefore, work done by Ajit and Rajat together in 'x' days = (11/60) * x
Step 4: Find the work remaining after Ajit and Rajat's work
The total work remaining after Ajit and Rajat's work = Total work - Work done by Ajit in 2 days - Work done by Ajit and Rajat together
Total work = 1 (as it represents the whole work)
Work done by Ajit in 2 days = 1/5 (from Step 2)
Work done by Ajit and Rajat together in 'x' days = (11/60) * x (from Step 3)
Work remaining = 1 - 1/5 - (11/60)x = 4/5 - (11/60)x
Step 5: Find the time taken by Abhay to complete the remaining work
Abhay's efficiency = 1/15
Let's assume Abhay takes 'y' days to complete the remaining work.
Therefore, work done by Abhay in 'y' days = (1/15) * y
Step 6: Form an equation using the remaining work
The remaining work is the same as the work done by Abhay in 'y' days.
Therefore, 4/5 - (11/60)x = (1/15) * y
Step 7: Solve the equation to find the value of 'y'
4/5 - (11/60)x = (1/15) * y
We know that the work gets completed in 35/4 days.
Therefore, y = 35/4 - 2 - x (subtracting 2 days worked by Ajit and the
- Ajit can do the work in 10 days.
- Rajat can do the work in 12 days.
- Abhay can do the work in 15 days.
- Ajit works for 2 days.
- Then Rajat joins and they work together for some days.
- Finally, Abhay completes the remaining work.
- The total time taken to complete the work is 35/4 days.
- They get ₹5000 for the work.
Let's solve the problem step by step.
Step 1: Calculate the efficiency of each person
Efficiency is defined as the amount of work done in one day.
- Ajit's efficiency = 1/10 (as he can complete the work in 10 days)
- Rajat's efficiency = 1/12 (as he can complete the work in 12 days)
- Abhay's efficiency = 1/15 (as he can complete the work in 15 days)
Step 2: Find the work done by Ajit in 2 days
Ajit's efficiency = 1/10
Therefore, work done by Ajit in 2 days = (1/10) * 2 = 1/5
Step 3: Find the work done by Ajit and Rajat together
Ajit and Rajat work together for some days and complete a certain amount of work. Let's assume they work together for 'x' days.
Ajit's efficiency = 1/10
Rajat's efficiency = 1/12
Their combined efficiency = 1/10 + 1/12 = 6/60 + 5/60 = 11/60
Therefore, work done by Ajit and Rajat together in 'x' days = (11/60) * x
Step 4: Find the work remaining after Ajit and Rajat's work
The total work remaining after Ajit and Rajat's work = Total work - Work done by Ajit in 2 days - Work done by Ajit and Rajat together
Total work = 1 (as it represents the whole work)
Work done by Ajit in 2 days = 1/5 (from Step 2)
Work done by Ajit and Rajat together in 'x' days = (11/60) * x (from Step 3)
Work remaining = 1 - 1/5 - (11/60)x = 4/5 - (11/60)x
Step 5: Find the time taken by Abhay to complete the remaining work
Abhay's efficiency = 1/15
Let's assume Abhay takes 'y' days to complete the remaining work.
Therefore, work done by Abhay in 'y' days = (1/15) * y
Step 6: Form an equation using the remaining work
The remaining work is the same as the work done by Abhay in 'y' days.
Therefore, 4/5 - (11/60)x = (1/15) * y
Step 7: Solve the equation to find the value of 'y'
4/5 - (11/60)x = (1/15) * y
We know that the work gets completed in 35/4 days.
Therefore, y = 35/4 - 2 - x (subtracting 2 days worked by Ajit and the
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Community Answer
Ajit, Rajat and Abhay can do a piece of work in 10, 12 and 15 days re...
Let the total units of work to be done be 60 units(LCM of 10,12 and 15)
Now Ajit does 6 units in 1 day, Rajat 5 and Abhay 4.
Now Initially Ajit worked for 2 two days so he would have completed 12 units of work.
So remaining work is 48 units and time is 35/4 - 2 = 27/4
11x + 4y = 48
x + y = 27/4
on solving we get x= 3 and y = 15/4
So in 15/4 Days Abhay will do 15/4 x 4 = 15 units of work.
So Abhay's share in work = 15/60 = 25%
So his share would be 25*5000/100 = Rs 1250.
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Ajit, Rajat and Abhay can do a piece of work in 10, 12 and 15 days respectively. Ajit works for two days and then Rajat joins him. They together work for some days and then leave. Abhay completes the remaining work. If work gets completed in 35/4 days and they get ₹ 5000 for the work, find the share of Abhay in the money.a)1250b)1500c)1000d)1200Correct answer is option 'A'. Can you explain this answer?
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Ajit, Rajat and Abhay can do a piece of work in 10, 12 and 15 days respectively. Ajit works for two days and then Rajat joins him. They together work for some days and then leave. Abhay completes the remaining work. If work gets completed in 35/4 days and they get ₹ 5000 for the work, find the share of Abhay in the money.a)1250b)1500c)1000d)1200Correct answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Ajit, Rajat and Abhay can do a piece of work in 10, 12 and 15 days respectively. Ajit works for two days and then Rajat joins him. They together work for some days and then leave. Abhay completes the remaining work. If work gets completed in 35/4 days and they get ₹ 5000 for the work, find the share of Abhay in the money.a)1250b)1500c)1000d)1200Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ajit, Rajat and Abhay can do a piece of work in 10, 12 and 15 days respectively. Ajit works for two days and then Rajat joins him. They together work for some days and then leave. Abhay completes the remaining work. If work gets completed in 35/4 days and they get ₹ 5000 for the work, find the share of Abhay in the money.a)1250b)1500c)1000d)1200Correct answer is option 'A'. Can you explain this answer?.
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