Question : A and B together finish a work in 6 days. If A alone can finish the work in 10 days, then in how many days B alone can complete the work?
Option 1: 15 days
Option 2: 10 days
Option 3: 12 days
Option 4: 14 days
Correct Answer: 15 days
Solution :
Time taken by A alone to do the work = 10 days
Part of work done by A in a day = $\frac{1}{10}$
Let $x$ be the time taken by B to do the work.
Part of work done by B in a day = $\frac{1}{x}$
Time taken by A and B together to do the work = 6 days
Part of work done by A and B in a day = $\frac{1}{6}$
So, $\frac{1}{10}$ + $\frac{1}{x}$ = $\frac{1}{6}$
⇒ $\frac{1}{x}$ = $\frac{1}{6}$ – $\frac{1}{10}$ = $\frac{10-6}{60}$ = $\frac{1}{15}$
⇒ $x$ = 15 days
Hence, the correct answer is 15 days.
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