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Time & Work

A certain number of men do a piece of work in 40 days. If there has been 45 men more, the work could have been finished in 25 days. The original number of men employed at the work were

Option:
A. 75
B. 60
C. 45
D. 30
Answer: A . 75

Justification:

Suppose originally there were x men.
x men can finish a job in = 40 days.
1 man can finish a job in = 40 x $x$
So. $(x + 45)$ men can do a job in = ${40 × x}/{x + 45}$ days
By hypotheses,
=${40x}/{x + 45}$ = 25
or $40x$ = $25x$ + 1125
or $15x$ = 1125
$x$ = 75 men.
Hence, originally there was 75 men. 

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