Question : A contractor decided to complete a work in 80 days and employed 60 men at the beginning and 20 men additionally after 20 days and got the work completed as per schedule. If he had not employed the additional men, how many extra days would he have needed to complete the work (round off to the nearest integer)?
Option 1: 32 days
Option 2: 20 days
Option 3: 30 days
Option 4: 26 days
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Correct Answer: 20 days
Solution :
Given, the time taken to complete the work = 80 days
Number of days 60 men worked together = 20 days
Number of days 80 men worked together = 60 days
Let the work done by a man in a day be $x$ units.
According to the question,
$60\times 20 \times x + 80\times 60\times x=1$
⇒ $1200x + 4800x = 1$
⇒ $x = \frac{1}{6000}$
So, total work done by 60 men in a day = $\frac{60}{6000}=\frac{1}{100}$
Time taken by 60 men to complete the work = 100 days
Extra days taken = 100 – 80 = 20 days
Hence, the correct answer is 20 days.
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