Q. If A and B together can complete a work in 18 days, A and C together in 12 days and B and C together in 9 days, then in how many days B alone can do the work?
Answer: 24 days
Notes: (A + B)'s 1 day's work $latex = \frac{1}{18}&s=1$
(B + C)'s 1 day's work $latex = \frac{1}{9}&s=1$
(C + A)'s 1 day's work $latex = \frac{1}{12}&s=1$
On adding all above equations, we get
2 (A +B + C)'s 1 day's work $latex = \frac{1}{18} + \frac{1}{9} + \frac{1}{12} = \frac{2+4+3}{36} = \frac{9}{36} = \frac{1}{4}&s=1$
∴ (A + B + C)'s 1 day's work $latex = \frac{1}{8}&s=1$
Now, B's 1 day's work = (A + B + C)'s 1 day's work - (A + C)'s 1 day's work
$latex = \frac{1}{8}-\frac{1}{12}=\frac{3-2}{24}=\frac{1}{24}&s=1$
Hence B alone can do the work in 24 days. So option [B] is correct answer
