Question
Download Solution PDFA 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Time taken by (man + woman) = (1/2) × Time taken by (woman + boy)
A boy alone can finish the work = 20 days
2 women can finish the work = 30 days.
Concept used:
If total work is constant then,
Time ∝ (1/efficiency)
Formula used:
Total work = efficiency × time
Calculation:
2 women can finish the work = 30 days.
1 woman can finish the work = 30 × 2 = 60 days
| Efficiency | Person | Time | Total work |
| 1 | Woman | 60 | 60 |
| 3 | Boy | 20 |
Now,
Time taken by (man + woman) = (1/2) × Time taken by (woman + boy)
Time taken by (man + woman) : Time taken by (woman + boy) = 1 : 2
Efficiency of (man + woman) : Efficiency of (woman + boy) = 2 : 1
(Woman + boy) = (3 + 1) = 4
⇒ 1 unit = 4 units/day
⇒ 2 units = 4 × 2 = 8 units/day
Efficiency of (man + woman) = 8
Efficiency of man = 8 - 1 = 7 units/day
Time taken to complete the work by 4 men = 60/(4 × 7)
⇒ 60/28 = 15/7 = 2.14 days
∴ The correct answer is 2.14 days.
Last updated on Jul 22, 2025
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