Question : A company employed 200 workers to complete a certain task in 150 days. If only one-fourth of the work has been done in 50 days. Then, in order to complete the whole work on time, the number of additional workers to be employed was:
Option 1: 100
Option 2: 300
Option 3: 600
Option 4: 200
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Correct Answer: 100
Solution :
Given: Men employed initially $(M_1) = 200$
Let total men required to complete the work = $M_2$
Total days = 150
Work done in days $(D_1) = 50$
Remaining days $(D_2) = 100$
Work completed $(W_1) = \frac{1}{4}$
Remaining work $(W_2) = \frac{3}{4}$
We know that,
$\frac{M_1\times D_1}{W_1}=\frac{M_2\times D_2}{W_2}$
Putting the values, we get
⇒ $\frac{200\times 50}{\frac{1}{4}}=\frac{M_2\times 100}{\frac{3}{4}}$
⇒ $M_2=300$
Additional men required = 300 – 200 = 100
Hence, the correct answer is 100.
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