Five men and 2 boys can do in 30 days as much work as 7 men and 10 boys can do in 15 days. How many boys should join 40 men to do the same work in 4 days?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e.10
Let the work done in one day by a man = m and by a boy = b
According to the given question,
30 × (5m + 2b) = 15 × (7m + 10b)
⇒ 2 × (5m + 2b) = (7m + 10b)
⇒ 10m + 4b = 7m + 10b
⇒ 3m = 6b ⇒ m = 2b
Thus, a man can do as much work in a day done by two boys in a day.
Let the m = 2, b = 1 and the number of boys required = B
So, 30 × (5m + 2b) = 4 × (40m + B)
⇒ 30 × (10 + 2) = 4 × (80 + B)
⇒ 30 × 12 = 4 × (80 + B)
⇒ 30 × 3 = 80 + B ⇒ B = 90 - 80 = 10