Question : A, B, and C can complete a work in 10, 12, and 15 days respectively. They started the work together, but A left the work before five days of its completion. B also left the job two days after A left. In how many days was the work completed?
Option 1: 4 days
Option 2: 5 days
Option 3: 7 days
Option 4: 8 days
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Correct Answer: 7 days
Solution : A left the work 5 days before completion. B left the work 3 days before completion. We know that Total work = Number of days × Efficiency of work. Let the number of days required to complete the whole work = $x$ and the whole work is 1. 1 day work of A = $\frac{1}{10}$ 1 day work of B = $\frac{1}{12}$ 1 day work of C = $\frac{1}{15}$ According to the question, $\frac{x-5}{10} + \frac{x-3}{12} + \frac{x}{15} = 1$ $⇒6(x-5)+5(x-3)+4x = 60$ $⇒6x-30+5x-15+4x =60$ $⇒15x-45 = 60$ $⇒15x=105$ $\therefore x=7$ Hence, the correct answer is 7 days.
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