Q. 374.2( 12 Votes )

2 men and 5 boys can finish a piece of work in 4 days, while 3 men and 6 boys can finish it in 3 days. Find the time taken by one man alone to finish the work and that taken by one boy alone to finish the work.

Answer :

1st Method


Let the time taken by one man alone to finish the work and that taken by one boy alone to finish the work be u and v days respectively.


Time taken by 1 man to finish one part of the work = 1/u days


Time taken by 1 boy to finish one part of the same work = 1/v days


According to question -

2 men and 5 boys can finish a piece of work in 4 days. Therefore, to finish one part of work they will take 1/4 days

.....(1)

Similarly, 3 men and 6 boys can finish the same work in 3 days. Therefore, to finish one part of work they will take 1/3 days

.....(2)

Multiplying equation (1) by 3 and equation (2) by 2 and using the elimination method, we have


v = 36


Substituting the value of v in equation (1), we get -


u = 18


Thus, time taken by one man to finish the work alone = 18 days


and, time taken by one boy to finish the work alone = 36 days


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