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Question

Two men and 5 boys together can finish a piece of work in 4 days, while 3 men and 6 boys can finish in 3 days. Find the time taken :
(i) by one man alone to finish the work
(ii) by one boy alone to finish the work.

A
17 days and 19 days
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B
14 days and 22 days
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C
18 days and 36 days
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D
17 days and 13 days
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Solution

The correct option is C 18 days and 36 days
Let the amount of work done by a Man alone in a day be M and by a Boy alone be B
Given, 2 men and 5 boys together can finish a piece of work in 4 days
Amount of work they can do in one day 2M+5B=14 -- (1)
Similarly, 3M+6B=13 --- (2)
Solving equations (1) and (2), we get B=136
Substituting B in equation 2, we get M=118
Hence, one man alone will take 18 days to do the work and one boy will take 36 days.


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