Question : A, B, and C can separately do work in 6, 10, and 15 days respectively. They started to work together but C left after 2 days. In how many days will the remaining work be finished?
Option 1: $1 \frac{2}{4}$
Option 2: $1 \frac{1}{4}$
Option 3: $1 \frac{5}{8}$
Option 4: $2 \frac{7}{4}$
Correct Answer: $1 \frac{1}{4}$
Solution :
Given, A, B, and C can separately do a work in 6, 10, and 15 days, respectively.
Work done by A in a day= $\frac{1}{6}$
Work done by B in a day = $\frac{1}{10}$
Work done by C in a day = $\frac{1}{15}$
Work done by A, B, and C together in a day = $\frac{1}{6}+\frac{1}{10}+\frac{1}{15}$ = $\frac{1}{3}$
Work done by A, B, and C together in 2 days = $\frac{2}{3}$
Work left for A and B to do = $1-\frac{2}{3}=\frac{1}{3}$
Work done by A and B together in 1 day = $\frac{1}{6}+\frac{1}{10}=\frac{4}{15}$
$\therefore$ Time taken by them to complete the work = $\frac{\frac{1}{3}}{\frac{4}{15}}$ = $\frac{5}{4}$ days
Hence, the correct answer is $1\frac{1}{4}$ days.
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