Question : A and B can complete a work in 10 and 16 days respectively. A begins to do the work and they work alternatively one at a time for one day each. The whole work will be completed in:
Option 1: $12 \frac{1}{4}$ days
Option 2: $13 \frac{1}{4}$ days
Option 3: $15 \frac{1}{4}$ days
Option 4: $14 \frac{1}{4}$ days
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Correct Answer: $12 \frac{1}{4}$ days
Solution : Given, A and B can complete a piece of work in 10 and 16 days, respectively. Work done by A in a day = $\frac{1}{10}$ Work done by B in a day = $\frac{1}{16}$ ⇒ Work done by A and B in 2 days if they work alternatively = $\frac{1}{10}+\frac{1}{16}=\frac{13}{80}$ ⇒ Work done by A and B in 12 days if they work alternatively = $\frac{13}{80}×6=\frac{39}{40}$ ⇒ Work left after 12 days = $1-\frac{39}{40}=\frac{1}{40}$ ⇒ Time taken by A to complete remaining work = $\frac{\frac{1}{40}}{\frac{1}{10}}=\frac{1}{4}$ days $\therefore$ Total time = $12+\frac{1}{4}=12\frac{1}{4}$ days Hence, the correct answer is $12\frac{1}{4}$ days.
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