Question : A man alone can do a piece of work in 16 days, but with the help of his friend, he can do it in 8 days. In what time can his friend do it alone?
Option 1: 12 days
Option 2: 14 days
Option 3: 16 days
Option 4: 10 days
Correct Answer: 16 days
Solution :
Time taken by a man to do the work = 16 days
Part of done by the man in a day = $\frac{1}{16}$
Let $x$ be the time taken by the friend to do the work.
Part of work done by the friend in a day = $\frac{1}{x}$
Time taken by the man and his friend together to do the work = 8 days
Part of done by the man and his friend together in a day = $\frac{1}{8}$
$\frac{1}{16}$ + $\frac{1}{x}$ = $\frac{1}{8}$
⇒ $\frac{1}{x}$ = $\frac{1}{8}$ – $\frac{1}{16}$ = $\frac{2-1}{16}$ = $\frac{1}{16}$
⇒ $x$ = 16 days
Hence, the correct answer is 16 days.
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