A and B together can do a piece of work in 10 days, while B and C together can do it in 12 days and C and A together in 15 days. In how many days C would complete it alone?
A and B together can do a piece of work in 10 days, while B and C together can do it in 12 days and C and A together in 15 days. In how many days C would complete it alone?
[A]24 days
[B]30 days
[C]40 days
[D]60 days
40 days
(A + B)’s 1 day’s work $latex = \frac{1}{10}&s=1$……(I)
(B + C)’s 1 day’s work $latex = \frac{1}{12}&s=1$……(II)
(C + A)’s 1 day’s work $latex = \frac{1}{15}&s=1$……(III)
On adding all the equations,
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 $latex = \frac{1}{8}&s=1$……(IV)
Now, C’s 1 day’s work = (A + B + C)’s 1 day’s work – (A + B)’s 1 day’s work
$latex = \frac{1}{8}-\frac{1}{10}=\frac{5-4}{40}=\frac{1}{40}&s=1$
Hence C will finish the work in 40 days. So option [C] is correct answer.