Q. A and B can do a piece of work in 10 days. B and C can do it in 12 days. A and C can do it in 15 days. How long will A take to do it alone?
Answer: 24 days
Notes: (A + B)'s 1 day's work $latex = \frac{1}{10}&s=1$
(B + C)'s 1 day's work $latex = \frac{1}{12}&s=1$
(C + A)'s 1 day's work $latex = \frac{1}{15}&s=1$
On adding,
2(A + B + C)'s 1 day's work $latex = \frac{1}{10}+\frac{1}{12}+\frac{1}{15} = \frac{6+5+4}{60} = \frac{1}{4}&s=1$
∴ (A + B + C)'s 1 day's work $latex = \frac{1}{8}&s=1$
∴ A's 1 day's work $latex = \frac{1}{8}-\frac{1}{12} = \frac{3-2}{24} = \frac{1}{24}&s=1$
∴ A alone will complete the work in 24 days.
Hence option [B] is correct answer.
