8 men and 3 boys together can complete a piece of work in 5 days. If 5 boys can complete the same piece of work in 15 days, in how many days do 5 men complete the same piece of work?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 10
Measure the whole job in boy-days (the work one boy does in one day), then find how many boys one man is worth.
The whole job (5 boys take 15 days):
Work \(=5\times15=75\) boy-days
One man in boys (8 men and 3 boys finish it in 5 days):
The 3 boys do \(3\times5=15\) boy-days, so the 8 men do \(75-15=60\) boy-days in 5 days
8 men do 12 boy-days of work a day, so 1 man = 1.5 boys
Time for 5 men:
5 men \(=5\times1.5=7.5\) boys
Days \(\displaystyle =\frac{75}{7.5}=10\)