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1. X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

A. 6 days

B. 10 days

C. 15 days

D. 20 days

Solution:

\begin{aligned} work done by X in 4 days \\ = \frac{1}{20} \times 4 = \frac{1}{5} \\ Remaining work \\ = 1 - \frac{1}{5} = \frac{4}{5} \\ (X + Y)'s 1 day's work \\ = \frac{1}{20} + \frac{1}{12} = \frac{8}{60} = \frac{2}{15} \\ Now, \frac{2}{15} work is done by X and Y in 1 day . \\ So, \frac{4}{5} work will be done by X and Y in \\ \frac{15}{2} \times \frac{4}{5} = 6 days \\ Hence, total time taken \\ = (6 + 4) days \\ = 10 days \end{aligned}

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