Question
Download Solution PDF12 men and 16 boys can do a piece of work in 5 days, while 13 men and 24 boys can do it in 4 days. In how many days can 29 men and 22 boys complete the work?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
(12 men + 16 boys) can do a piece of work = 5 days
(13 men + 24 boys) can do a piece of work = 4 days
Formula used:
Total work = efficiency × time
Calculation:
Let, the efficiency of man = M
The efficiency of boy = B
According to the question:
⇒ (12 M + 16 B) × 5 = (13 M + 24 B) × 4
⇒ 60 M - 52 M = 96 B - 80 B
⇒ 8 M = 16 B
⇒ M/B = 2/1
Total work = (12 M + 16 B) × 5
⇒ {(12 × 2) + (16 × 1)} × 5
⇒ (24 + 16) × 5 = 40 × 5 = 200 units
Required time to complete the work = 200/{(29 × 2) + (22 × 1)}
⇒ 200/(58 + 22) = 200/80
⇒ 5/2 = 2.5 days
∴ The correct answer is 2.5 days.
Last updated on Jul 10, 2025
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