A man and a woman can finish a work together in half the time taken by a woman and a boy together. A boy can finish the work alone in 20 days and 2 women together can finish it in 30 days. In how many days will the work be finished by 4 men?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 2.14.
Given:
Time taken (Man + Woman) = 1/2 × (Woman + Boy)
Concept used:
If work is constant,
Time is inversely proportional to efficiency
Calculations:
1 Boy completes the work = 20 days
2 woman can complete the work = 30 days
1 woman completes the work = 60 days
Total work (LCM of 30 and 60) = 60 units
Efficiency of a Boy = 60/20 = 3
Efficiency of a woman = 60/60 = 1
We know that,
⇒ Efficiency of (Man + Woman) : Efficiency of (Woman + Boy) = 2 : 1
According to the question;
⇒ 1 unit = 4 units/day
Efficiency of (Man + Woman) = 2 units = 8
Efficiency of man = 8 - 1 = 7 units/day
Required time taken by 4 men = 60/(4 × 7)
⇒ 60/28 = 2.14 days