A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The total time taken for the work to be completed was

8 days

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12 days

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10 days

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15 days

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Solution

The correct option is B
12 days

(A + B)'s 1 day's work = $\frac{1}{15}$ + $\frac{1}{10}$ = $\frac{1}{6}$

Work done by A and B in 2 days = $\frac{1}{6}$ × 2 = $\frac{1}{3}$

Remaining work = 1 - $\frac{1}{3}$ = $\frac{2}{3}$

Now, $\frac{1}{15}$ work is done by A in 1 day.

So, $\frac{2}{3}$ work will be done by A in 15 × $\frac{2}{3}$ = 10 days

Hence, the total time taken = 10 + 2 = 12 days.

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