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: 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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