Question : A and B can do a piece of work in 72 days. B and C can do it in 120 days and A and C can do it in 90 days. A alone can do it in:
Option 1: 120 days
Option 2: 130 days
Option 3: 150 days
Option 4: 100 days
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Correct Answer: 120 days
Solution : Given: Time taken by A and B to do the work = 72 days ⇒ Part of work done by A and B in a day = $\frac{1}{72}$ Time taken by B and C to do the work = 120 days ⇒ Part of work done by B and C in a day = $\frac{1}{120}$ Time taken by A and C to do the work = 90 days ⇒ Part of work done by A and C in a day = $\frac{1}{90}$ ⇒ Part of work done by A, B, and C in a day = $\frac{1}{2}[\frac{1}{90}+\frac{1}{120}+\frac{1}{72}]$ = $\frac{1}{2}[\frac{4+3+5}{360}]$ = $\frac{1}{60}$ So, part of work done by A alone = $\frac{1}{60}$–$\frac{1}{120}$ = $\frac{1}{120}$ Therefore, the time taken by A alone to do the work = 120 days Hence, the correct answer is 120 days.
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