If a certain number of workmen can do a piece of work in 25 hours, in how many hours will another set of an equal number of men, do a piece of work, twice as great, supposing that 2 men of the first set can do as much work in an hour, as 3 men of the second set do in an hour? `60` b. `\ 75` c. `90` d. `105`

Options

A. 60
B. 75
C. 90
D. 105

Answer

(b)

Explanation

Given : `2m_(1) = 3 M_(2')`
`therefore Efficiency: M_(1)/M_(2) = 3/2`
Let number of men in second group `= n` and hours
needed by them `= h`
`therefore` Total work by first group `= efficiency xx hour xx M_(1)`
`= 3 xx 35 xx n`
Also, `2(1^(st) group work) = 2^(n)` group work
` rArr 2 (3xx25xxn) = 2 xx n xx h`
`rArr h = 75 `