Question : A and B together can do a piece of work in 12 days, while A alone can do the same work in 30 days. B alone can do it in:
Option 1: 18 days
Option 2: 20 days
Option 3: 15 days
Option 4: 22 days
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Correct Answer: 20 days
Solution :
Given:
Time taken by A and B together to complete the work = 12 days
⇒ Part of work done by A and B in a day = $\frac{1}{12}$
Time taken by A alone to complete the work = 30 days
⇒ Part of work done by A alone in a day = $\frac{1}{30}$
Let the time taken by B alone to do the job = $x$ days
⇒ Part of the job done by B alone in 1 day = $\frac{1}{x}$
So, $\frac{1}{30}$ + $\frac{1}{x}$ = $\frac{1}{12}$
⇒ $\frac{1}{x}$ = $\frac{1}{12}$ — $\frac{1}{30}$ = $\frac{5 - 2}{60}$ = $\frac{1}{20}$
So, the time taken by B alone to complete the work = $x$ = 20 days
Hence, the correct answer is 20 days.
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