A and B together can complete a piece of work in 72 days, B and C together can complete it in 120 days, and A and C together in 90 days. In what time can A alone complete the work?
A and B together can complete a piece of work in 72 days, B and C together can complete it in 120 days, and A and C together in 90 days. In what time can A alone complete the work?
[A]150 days
[B]80 days
[C]100 days
[D]120 dyas
120 days
(A+B)’s 1 day’s work = $latex \frac{1}{72}&s=1$
(B+C)’s 1 day’s work = $latex \frac{1}{120}&s=1$
(C+A)’s 1 day’s work = $latex \frac{1}{90}&s=1$
Adding all three, 2(A+B+C)’s 1 days work = $latex \frac{1}{72}+\frac{1}{120}+\frac{1}{90}&s=1$
$latex => \frac{5+3+4}{360}=\frac{12}{360}=\frac{1}{30}&s=1$
∴ (A+B+C)’s 1 day’s work = $latex \frac{1}{60}&s=1$
Now, A’s 1 day’s work = (A+B+C)’s 1 day’s work – (B+C)’s 1 day’s work
$latex =>\frac{1}{60}-\frac{1}{120}=\frac{2-1}{120}=\frac{1}{120}&s=1$
∴ A alone can comlete the work in 120 days.
Hence option [D] is correct.