Correct Answer: 12 days

Solution : Given,
A and B together can complete a work in 20 days
⇒ Work done by A and B together in 1 day = $\frac{1}{20}$
Also, B and C together can complete the same work in 15 days
⇒ Work done by B and C together in 1 day = $\frac{1}{15}$
A, B, and C all work together and the same work gets completed in 10 days
⇒ Work done by A, B, and C together in 1 day = $\frac{1}{10}$
For one day,
⇒ Work done by C + Work done by A and B together = $\frac{1}{10}$
⇒ Work done by C + $\frac{1}{20}=\frac{1}{10}$
⇒ Work done by C = $\frac{1}{10}-\frac{1}{20}$ = $\frac{1}{20}$
And, Work done by A + Work done by B and C together = $\frac{1}{10}$
⇒ Work done by A + $\frac{1}{15}=\frac{1}{10}$
⇒ Work done by A = $\frac{1}{10}-\frac{1}{15}$
⇒ Work done by A = $\frac{3-2}{30}$
⇒ Work done by A = $\frac{1}{30}$
$\therefore$ Work done by A and C in one day together = $\frac{1}{20}+\frac{1}{30}=\frac{3+2}{60}=\frac{1}{12}$
⇒ They will take 12 days to complete the work.
Hence, the correct answer is 12 days.