Question : 12 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?
Option 1: 2.5
Option 2: 2.45
Option 3: 2.6
Option 4: 2.4
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Correct Answer: 2.5
Solution :
Given:
12 men and 16 boys can do a piece of work in 5 days.
So, 60 men and 80 boys can do the work in 1 day. ---(1)
13 men and 24 boys can do it in 4 days.
So, 52 men and 96 boys can do it in 1 day. ---(2)
From equations 1 and 2, we get,
60 men + 80 boys = 52 men + 96 boys
⇒ 8 men = 16 boys
⇒ 1 man = 2 boys
So, 12 men = 24 boys
So, (24 + 16) = 40 boys can do the work in 5 days.
29 men = 29 × 2 = 58 boys
So, (58 + 22) = 80 boys can do the work in $\frac{40×5}{80}=2.5$ days.
Hence, the correct answer is 2.5.
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