Question : A work can be completed by 8 boys in 48 days. If 2 boys leave after working for 24 days, then how many days will be needed to complete the remaining work?
Option 1: 20 days
Option 2: 24 days
Option 3: 32 days
Option 4: 30 days
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Correct Answer: 32 days
Solution : $⇒m_1d_1 = m_2d_2$ Given that 8 boys can complete the work in 48 days if 2 boys leave after working for 24 days, the number of boys for the first 24 days $m_1$ is 8, and the number of boys for the remaining days $m_2$ is 6. The number of days for the first part $d_1$ is 24. We want to find the number of days for the remaining part $d_2 $ . $⇒ (8 × 48) = (8 × 24) + 6d_2 $ $⇒ d_2 = \frac{(8 × 48) - (8 × 24)}{6} = 32$ Hence, the correct answer is 32 days.
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