Q. A and B can do a piece of work in 72 days. B and C can do it in 120 days, A and C can do it in 90 days. In how many days all the three together can do the work ?
Answer: 60 days
Notes: According to question,
(A + B)'s one day's work $latex = \frac{1}{72}&s=1$
(B + C)'s one day's work $latex = \frac{1}{120}&s=1$
and (C + A)'s one day's work $latex = \frac{1}{90}&s=1$
On adding all three,
2 (A + B + C)'s one day's work $latex = \frac{1}{72}+ \frac{1}{120}+ \frac{1}{90}&s=1$
$latex = \frac{5+3+4}{360} = \frac{1}{30}&s=1$
∴ (A + B + C)'s one day's work $latex = \frac{1}{60}&s=1$
∴ A, B and C together can finish the whole work in 60 days.
Hence option [B] is the right answer.
