If A and B together can complete a work in 12 days, B and C together in 15 days and C and A together in 20 days, then in how many days can B alone complete the work :
If A and B together can complete a work in 12 days, B and C together in 15 days and C and A together in 20 days, then in how many days can B alone complete the work :
[A]20 days
[B]24 days
[C]25 days
[D]30 days
20 days
(A + B)’s 1 day’s work $latex = \frac{1}{12}&s=1$
(B + C)’s 1 day’s work $latex = \frac{1}{15}&s=1$
(C + A)’s 1 day’s work $latex = \frac{1}{20}&s=1$
On adding all above equations,
2(A + B + C)’s 1 day’s work $latex = \frac{1}{12}+\frac{1}{15}+\frac{1}{20}&s=1$
$latex = \frac{5+4+3}{60} = \frac{1}{5}&s=1$
∴ (A + B + C)’s 1 day’s work $latex = \frac{1}{10}&s=1$
∴ B’s 1 day’s work $latex = \frac{1}{10}-\frac{1}{20} = \frac{2-1}{20} = \frac{1}{20}&s=1$
∴ B alone can do the work in 20 days.
Hence option [A] is correct answer.