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3 men and 4 boys can di a piece of work in 14 days, while 4 men and 6 boys can do it in 12 days. How long would it take 1 boys to finish the work.?
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3 men and 4 boys can di a piece of work in 14 days, while 4 men and 6 ...
Understanding the Problem
To solve the problem, we need to determine the work rates of men and boys. We have two scenarios:
- Scenario 1: 3 men and 4 boys can complete the work in 14 days.
- Scenario 2: 4 men and 6 boys can complete the work in 12 days.
Calculating Total Work
- Total work can be expressed in terms of "man-days" or "boy-days".
For Scenario 1:
- Work done = (3 men + 4 boys) * 14 days
For Scenario 2:
- Work done = (4 men + 6 boys) * 12 days
Setting Up Equations
Let the work rate of 1 man be M and that of 1 boy be B.
- From Scenario 1:
- 14 * (3M + 4B) = Total Work (W)
- From Scenario 2:
- 12 * (4M + 6B) = Total Work (W)
Since both expressions equal the same total work, we can set them equal to each other:
14 * (3M + 4B) = 12 * (4M + 6B)
Simplifying the Equation
- Expand both sides:
- 42M + 56B = 48M + 72B
- Rearranging gives:
- 6M = 16B
- Therefore, M = (8/3)B
Finding Individual Work Rates
Now substituting M back into one of the total work equations:
- Total work (W) can be expressed in terms of B:
- W = 14 * (3(8/3)B + 4B) = 14 * (8B + 4B) = 14 * 12B = 168B
Calculating Time for 1 Boy
To find how long it takes for 1 boy to finish the work alone:
- Time taken by 1 boy = Total work / Work rate of 1 boy
- Time = 168B / B = 168 days
Conclusion
Therefore, it would take 168 days for 1 boy to finish the work alone.
To solve the problem, we need to determine the work rates of men and boys. We have two scenarios:
- Scenario 1: 3 men and 4 boys can complete the work in 14 days.
- Scenario 2: 4 men and 6 boys can complete the work in 12 days.
Calculating Total Work
- Total work can be expressed in terms of "man-days" or "boy-days".
For Scenario 1:
- Work done = (3 men + 4 boys) * 14 days
For Scenario 2:
- Work done = (4 men + 6 boys) * 12 days
Setting Up Equations
Let the work rate of 1 man be M and that of 1 boy be B.
- From Scenario 1:
- 14 * (3M + 4B) = Total Work (W)
- From Scenario 2:
- 12 * (4M + 6B) = Total Work (W)
Since both expressions equal the same total work, we can set them equal to each other:
14 * (3M + 4B) = 12 * (4M + 6B)
Simplifying the Equation
- Expand both sides:
- 42M + 56B = 48M + 72B
- Rearranging gives:
- 6M = 16B
- Therefore, M = (8/3)B
Finding Individual Work Rates
Now substituting M back into one of the total work equations:
- Total work (W) can be expressed in terms of B:
- W = 14 * (3(8/3)B + 4B) = 14 * (8B + 4B) = 14 * 12B = 168B
Calculating Time for 1 Boy
To find how long it takes for 1 boy to finish the work alone:
- Time taken by 1 boy = Total work / Work rate of 1 boy
- Time = 168B / B = 168 days
Conclusion
Therefore, it would take 168 days for 1 boy to finish the work alone.
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3 men and 4 boys can di a piece of work in 14 days, while 4 men and 6 boys can do it in 12 days. How long would it take 1 boys to finish the work.?
Question Description
3 men and 4 boys can di a piece of work in 14 days, while 4 men and 6 boys can do it in 12 days. How long would it take 1 boys to finish the work.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 3 men and 4 boys can di a piece of work in 14 days, while 4 men and 6 boys can do it in 12 days. How long would it take 1 boys to finish the work.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3 men and 4 boys can di a piece of work in 14 days, while 4 men and 6 boys can do it in 12 days. How long would it take 1 boys to finish the work.?.
3 men and 4 boys can di a piece of work in 14 days, while 4 men and 6 boys can do it in 12 days. How long would it take 1 boys to finish the work.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 3 men and 4 boys can di a piece of work in 14 days, while 4 men and 6 boys can do it in 12 days. How long would it take 1 boys to finish the work.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3 men and 4 boys can di a piece of work in 14 days, while 4 men and 6 boys can do it in 12 days. How long would it take 1 boys to finish the work.?.
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