Question : A, B, and C can complete a work in 10, 12 and 15 days respectively. A left the work 5 days before the work was completed and B left 2 days after A had left. Number of days required to complete the whole work is:
Option 1: $8\frac{2}{3}$
Option 2: $6\frac{2}{3}$
Option 3: $7$
Option 4: $6$
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Correct Answer: $7$
Solution : Given: A, B, and C can complete a work in 10, 12, and 15 days respectively. A left the work 5 days before the work was completed and B left 2 days after A had left. Let total work = LCM of 10, 12, and 15 = 60 units [Use: Efficiency = $\frac{\text{Total Work}}{\text{Time}}$] So, A's efficiency = $\frac{60}{10}=6$ B's efficiency is = $\frac{60}{12}=5$ C's efficiency is = $\frac{60}{15}=4$ Let $n$ number of days required to complete the 60 units of work. According to the question, $6 \times(n-5) + 5 \times (n-3) + 4 n = 60$ ⇒ $6n-30+5n-15+4n=60$ ⇒ $15n = 105$ ⇒ $n=7$ Hence, the correct answer is $7$.
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