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?
Q. 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?
Answer: 120 days
Notes: (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