Question : 12 men can do work in 8 days while 4 boys can do it in 40 days. In how many days 9 boys and 3 men together will complete the same work?
Option 1: 10 days
Option 2: $\frac{280}{13}$ days
Option 3: $\frac{80}{7}$ days
Option 4: $\frac{260}{17}$ days
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Correct Answer: $\frac{80}{7}$ days
Solution : 12 men can do work in 8 days while 4 boys can do it in 40 days. $M_{1}D_{1} = M_{2}D_{2}$ $⇒ 12 \text{ men} \times 8 = 4 \text{ boys} \times 40$ $⇒ 12 \text{ men} = 4 \text{ boys} \times\frac{40}{8}$ $⇒ 3 \text{ men} = 5 \text{ boys}$ $⇒ 1 \text{ man} = \frac{5}{3} \text{ boys}$ Now in the second case, 4 boys can do work in 40 days. 1 boy can do the work in 40 × 4 days = 160 days 9 boys and 3 men = $9 + \frac{5}{3} \times 3$ boys 9 boys and 3 men = 14 boys 14 boys can do in = $\frac{160}{14} = \frac{80}{7}$ days. Hence, the correct answer is $\frac{80}{7}$ days.
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