Question : A and B together can do a piece of work in 36 days and B and C together can do it in 24 days. A and C together can do it in 18 days. The three working together can finish the work in:
Option 1: 8 days
Option 2: 16 days
Option 3: 30 days
Option 4: 32 days
Correct Answer: 16 days
Solution :
Given:
A and B together can do a piece of work in 36 days and B and C together can do it in 24 days. A and C together can do it in 18 days.
A and B together can do a piece of work in 36 days
⇒ A and B together in 1 day can do $\frac{1}{36}$ part of the work
B and C together can do a piece of work in 24 days
⇒ B and C together in 1 day can do $\frac{1}{24}$ part of the work
Also, A and C together can do a piece of work in 18 days
⇒ A and C together in 1 day can do $\frac{1}{18}$ part of the work
Now, A, B, and C together in 1 day can do $\frac{1}{2}(\frac{1}{36}+\frac{1}{24}+\frac{1}{18}$) part of the work
= $\frac{1}{2}(\frac{2+3+4}{72}$) = $\frac{9}{144}$ part of the work.
Therefore, the three working together can finish the work in (1 ÷ $\frac{9}{144}$) = $\frac{144}{9}$ = 16 days.
Hence, the correct answer is 16 days.
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