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.