Question : A alone can finish a work in 15 days. A works only for the first two days and the last two days. The rest work is done by B and the work is completed in 20 days. In how many days A and B together can finish the work?
Option 1: $\frac{90}{8}$
Option 2: $\frac{80}{7}$
Option 3: $\frac{80}{9}$
Option 4: $\frac{70}{8}$
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Correct Answer: $\frac{80}{9}$
Solution :
Time taken by A alone to do the work = 15
Work done by A alone in a day = $\frac{1}{15}$
Work done by A in the first and last two days = $\frac{4}{15}$
Work done by B in 16 days = 1 – $\frac{4}{15}$ = $\frac{11}{15}$
Work done by B alone in a day = $\frac{11}{15×16}$ = $\frac{11}{240}$
Work done by A and B together in a day
= $\frac{1}{15}$+$\frac{11}{240}$
= $\frac{27}{240}$
= $\frac{9}{80}$
$\therefore$ Time taken by A and B together to do the work = $\frac{80}{9}$ days
Hence, the correct answer is $\frac{80}{9}$.
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