Question : A and B can do a piece of work in 15 days. B and C can do the same work in 10 days and A and C can do the same in 12 days. The time taken by A, B and C together to do the job is:
Option 1: 4 days
Option 2: 9 days
Option 3: 8 days
Option 4: 5 days
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Correct Answer: 8 days
Solution :
Given: A and B can do a piece of work in 15 days. B and C can do the same work in 10 days also A and C can do the same in 12 days.
(A + B) in 1 day can do $\frac{1}{15}$ part of the work
(B + C) in 1 day can do $\frac{1}{10}$ part of the work
(C + A) in 1 day can do $\frac{1}{12}$ part of the work
So, the part of the work (A + B + C) can be done in 1 day,
= $\frac{1}{2}(\frac{1}{15}+\frac{1}{10}+\frac{1}{12})$
= $\frac{1}{2}(\frac{4+6+5}{60})$ = $\frac{15}{120}$
Therefore, the time taken by A, B, and C together to do the job is $(\frac{1}{\frac{15}{120}})=\frac{120}{15}$ = 8 days
Hence, the correct answer is 8 days.
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