Q. A and B can do a piece of work in 12 days. B and C in 8 days and C and A in 6 days. How long would B take to do the same work alone ?
Answer: 48 days
Notes: (A + B)'s 1 day's work $latex = \frac{1}{12}&s=1$……….(I)
(B + C)'s 1 day's work $latex = \frac{1}{8}&s=1$…….….(II)
(C + A)'s 1 day's work $latex = \frac{1}{6}&s=1$……….(III)
On adding,
2(A + B + C)'s 1 day's work $latex = \frac{1}{12}+\frac{1}{8}+\frac{1}{6} = \frac{2+3+4}{24} = \frac{9}{24}&s=1$
∴ (A + B + C)'s 1 day's work $latex = \frac{9}{24\times 2} = \frac{9}{48}&s=1$……….(IV)
On subtracting (III) from (IV),
B's 1 day's work $latex = \frac{9}{48} - \frac{1}{6}&s=1$
$latex = \frac{9-8}{48} = \frac{1}{48}&s=1$
∴ B can complete the work in 48 days.
Hence option [D] is correct answer.
