15 men and 21 women, working together, can do a job in 56 days, while 12 men and 24 women, working together, can do the same job in 64 days. In how many days can the same job be done by 18 men and 24 women, working together?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 47
Given:
15 men and 21 women, working together, can do a job in 56 days.
12 men and 24 women, working together, can do the same job in 64 days.
Calculations:
Let the efficiency of a man and a woman be M and W respectively
According to the question;
⇒ (15M + 21W) × 56 = (12M + 24W) × 64
⇒ 105M + 147W = 96M + 192W
⇒ 105M - 96M = 192W - 147W
⇒ 9M = 45W
⇒ M/W = 5/1
Now, Total work = (15M + 21W) × 56 = (15 × 5 + 21 × 1) × 56
Required time taken = [(15 × 5 + 21 × 1) × 56]/(18 × 5 + 24) = 896/19
⇒ 47