Question : A1 alone can do a work in 12 days and A2 alone can do the same work in 15 days. With help of A3, they finish the same work in 5 days. In how many days A3 alone can do the same work?
Option 1: 16
Option 2: 20
Option 3: 24
Option 4: 27
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Correct Answer: 20
Solution : Time taken by A1 to do the work = 12 days Part of work done by A1 in a day = $\frac{1}{12}$ Time taken by A2 to do the work = 15 days Part of work done by A2 in a day = $\frac{1}{15}$ Let $x$ be the time taken by A3 to do the work. Part of work done by A3 in a day = $\frac{1}{x}$ Time taken by A1, A2 and A3 to do the work = 5 days Part of work done by A1, A2 and A3 in a day = $\frac{1}{5}$ $\frac{1}{12}$ + $\frac{1}{15}$ + $\frac{1}{x}$ = $\frac{1}{5}$ ⇒ $\frac{1}{x}$ = $\frac{1}{5}$ – ($\frac{1}{12}$ + $\frac{1}{15}$) ⇒ $\frac{1}{x}$ = $\frac{12-5-4}{60}$ ⇒ $\frac{1}{x}$ = $\frac{3}{60}$ ⇒ $\frac{1}{x}$ = $\frac{1}{20}$ ⇒ $x$ = 20 days Hence, the correct answer is 20.
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