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?

A) 12

B) 20

C) 18

D) 24

Correct answer:
D) 24

Description for Correct answer:
Work done = \( \Large \frac{1}{3} \)

Remaining work = \( \Large \left(1-\frac{1}{3}\right)= \left(\frac{3-1}{3}\right)=\frac{2}{3} \)

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

More work, More men (Direct proportion)

More days, Less men (Indirect proportion)

Work \( \Large \frac{1}{3} \) : \( \Large \frac{2}{3} \)

:: 40 : (40+x)

Days 50 : 40

Therefore,

\( \Large \frac{1}{3} \times 50 \times \left(40+x\right) = \frac{2}{3} \times 40 \times 40 \)

\( \Large 5 \times \left(40+x\right) = 2 \times 40 \times 4 \)

200 + 5x = 320

5x = 320 - 200 = 120

Therefore, x = \( \Large \frac{120}{5} \) = 24

Therefore, Required number of men = 24


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