Question : A contractor was engaged to construct a road in 16 days. After working for 12 days with 20 labourers it was found that only $\frac{5}{8}$th of the road had been constructed. To complete the work in the stipulated time the number of extra labourers required is:
Option 1: 18
Option 2: 10
Option 3: 12
Option 4: 16
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Correct Answer: 16
Solution :
We know $\frac{M_1×D_1}{W_1}=\frac{M_2×D_2}{W_2}$
Where, $M_1$ = $M_2$ = Number of workers
$D_1$ = $D_2$ = Number of days
and $W_1$ = $W_2$ = Part of work.
Here, remaining work = $(1-\frac{5}{8})$ = $\frac{3}{8}$
and remaining days = (16 – 12) = 4 days
Now applying the above formula,
$\frac{20×12}{\frac{5}{8}}=\frac{M_2×4}{\frac{3}{8}}$
⇒ $M_2=\frac{20×12×3}{5×4}$
$\therefore M_2 = 36$
Therefore, to complete the work in the stipulated time the number of extra labourers required = (36 – 20) = 16
Hence, the correct answer is 16.
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