A certain amount of work can be done by a man, a woman and a boy in 20, 30 and 60 days, respectively. How many boys should be there in order to complete the work in 2 days with 2 men and 8 women?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 8 boys.
Time taken by a man to complete the work = 20 days
Time taken by a woman to complete the work = 30 days
Time taken by a boy to complete the work = 60 days
Part of the work was done by 2 men and 2 women in 2 days
⇒ 2 × (2/20 + 8/30)
⇒ 2 × (1/10 + 8/30)
⇒ 2 × (11/30)
⇒ 11/15
⇒ Amount of work remaining = 1 - (11/15) = 4/15
⇒ Work done by 1 boy in 2 days = 2/60 = 1/30
⇒ Number of boys required to assist = (4/15) × 30 = 8
∴ The number of boys required to complete the work in 2 days is 8