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1. 20 men complete one-third of a piece of work in 20 days. How many more men should be employed to finish the rest of the work in 25 more days ?

A. 10

B. 12

C. 15

D. 20

Solution:

Let the total number of men be x
Work done =

\frac{1}{3}

Remaining work
=

(1 - \frac{1}{3}) = \frac{2}{3}

More work, More men (Direct proportion)
More days, Less men (Indirect proportion)

\begin{matrix} Work \frac{1}{3} : \frac{2}{3} \\ Days 25 : 20 \end{matrix}} :: 20 : x

\begin{aligned} ∴ (\frac{1}{3} \times 25 \times x) = (\frac{2}{3} \times 20 \times 20) \\ \Leftrightarrow x = \frac{800}{25} \\ \Leftrightarrow x = 32 \end{aligned}

∴ More men to be employed = (32 - 20) = 12

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