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
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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