40 men complete one-third of a work in 40 days. How many more men should be employed to finish the rest of the work in 50 more days?

Correct Answer: 24

Work done = 1/3

Remaining work = (1−1/3)=(3−1/3)=2/3

Let the number of more men to be employed be x.

More work, More men (Direct proportion)

More days, Less men (Indirect proportion)

Work 1/3 : 2/3

:: 40 : (40+x)

Days 50 : 40

Therefore,

1/3×50×(40+x)=2/3×40×40

5×(40+x)=2×40×4

200 + 5x = 320

5x = 320 – 200 = 120

Therefore, x = 120/5 = 24

Therefore, Required number of men = 24