Question : 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 can all three together do the work?
Option 1: 80 days
Option 2: 100 days
Option 3: 60 days
Option 4: 150 days
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Correct Answer: 60 days
Solution : Given: 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. (A + B)'s 1 day's work = $\frac{1}{72}$ (B + C)'s 1 day's work = $\frac{1}{120}$ (A + C)'s 1 day's work = $\frac{1}{90}$ Adding the above three equations we get 2(A + B + C)'s 1 day's work = $\frac{1}{72}+\frac{1}{120}+\frac{1}{90} = \frac{5+3+4}{360} = \frac{12}{360} = \frac{1}{30}$ ⇒ (A + B + C)'s 1 day's work = $\frac{1}{60}$ $\therefore$ (A + B + C) together complete the work in 60 days. Hence, the correct answer is 60 days.
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