40 men can complete a work in 48 days. 56 men started for the same work for \(x\) days. After \(x\) days, 16 men increased, so, the remaining work is completed in \(13\frac{1}{3}\) days. Find \(x\)?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\frac{120}{7}\)
The work is measured in man-days: men × days. The whole work needs as many man-days as 40 men give in 48 days, and the work done in the two stages must add up to it.
Whole work: \(40\times48=1920\) man-days
First stage, 56 men for \(x\) days: \(56x\) man-days
Second stage, \(56+16=72\) men for \(13\frac{1}{3}=\frac{40}{3}\) days: \(72\times\frac{40}{3}=960\) man-days
The two stages make the whole work: \(56x+960=1920\)
This gives \(56x=960\), so \(\displaystyle x=\frac{960}{56}=\frac{120}{7}\) days