Question
Download Solution PDF15 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
15 men + 21 women can do a job = 56 days
12 men + 24 women can do a job = 64 days
Formula used:
Total work = efficiency × time
Calculation:
Let, the man efficiency = M
The woman efficiency = W
According to the question:
⇒ (15 M + 21 W) × 56 = (12 M + 24 W) × 64
⇒ (15 M + 21 W) × 7 = (12 M + 24 W) × 8
⇒ 105 M - 96 M = 192 W - 147 W
⇒ 9 M = 45 W
⇒ M/W = 5/1
Total work = (15 M + 21 W) × 56
⇒ {(15 × 5) + 21) × 56} = (96 × 56) units
Total efficiency = 18 M + 24 W
⇒ (18 × 5) + 24 × 1 = 114 units
Required time taken to complete work = Total work/total efficiency
⇒ (96 × 56)/114 = (16 × 56)/19 = 47
∴ The correct answer is 47
Last updated on Jul 15, 2025
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