Question : 8 men or 10 boys can complete a work in 174 days. 12 men and 14 boys will complete the same work in how many days?
Option 1: 60 days
Option 2: 50 days
Option 3: 72 days
Option 4: 84 days
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Correct Answer: 60 days
Solution :
Let M is the work done by one man in one day, B is the work done by one boy in one day and D is the number of days.
According to the problem, 8 men or 10 boys can complete the work in 174 days.
This means that the work done by 8 men in one day is equal to the work done by 10 boys in one day.
⇒ 8M = 10B ⇒ B = $\frac{4}{5}$M
The total work done as the work done by one man in one day times the number of days it takes for 8 men to complete the work:
⇒ Total work (W) = 8M × 174
The required days it would take for 12 men and 14 boys to complete the same work is D.
⇒ W = (12M + 14B) × D
Since both expressions are equal to W,
⇒ 8M × 174 = (12M + 14B) × D
Substituting B = $\frac{4}{5}$M from the first equation into the second equation gives,
⇒ 8M × 174 = (12M + 14 × $\frac{4}{5}$M) × D
⇒ D = $\frac{1392\times5}{116}$ = 60
Hence, the correct answer is 60 days.
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