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1. A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :

A. $\frac{1}{4}$

B. $\frac{1}{10}$

C. $\frac{7}{15}$

D. $\frac{8}{15}$

Solution:

\begin{aligned} A's 1 day's work = \frac{1}{15}; \\ B's 1 day's work = \frac{1}{20}; \\ (A + B)'s 1day's work \\ = \frac{1}{15} + \frac{1}{20} = \frac{7}{60} \\ (A + B)'s 4 day's work \\ = \frac{7}{60} \times 4 = \frac{7}{15} \\ ∴ Remaining work = 1 - \frac{7}{15} = \frac{8}{15} \end{aligned}

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