30 boys are engaged to do a piece of work in 15 days but it is found that in 5 days, 3/5 work is completed. How many boys may be allowed to go off, so that the work may be finished on time?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 20
Work can be measured in boy-days (number of boys × number of days): the same work always needs the same number of boy-days, however the boys are shared out.
The whole work (the work done so far is \(\frac{3}{5}\) of it):
Work done so far: 30 boys × 5 days \(=150\) boy-days
Whole work \(\displaystyle =150\times\frac{5}{3}=250\) boy-days
The work left (to be finished in the remaining \(15-5=10\) days):
Work left \(=250-150=100\) boy-days
Boys needed \(=100\div10=10\)
Boys who may go off \(=30-10=20\)