Question : A and B can do a piece of work in 18 days, B and C in 24 days and A and C in 36 days. Working together, they can do the work in:
Option 1: 12 days
Option 2: 13 days
Option 3: 16 days
Option 4: 26 days
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Correct Answer: 16 days
Solution :
One day work of (A + B) = $\frac{1}{18}$
One day work of (B + C) = $\frac{1}{24}$
One day work of (C + A) = $\frac{1}{36}$
Combined work = ($\frac{1}{A+B}+\frac{1}{B+C}+\frac{1}{C+A}$) = ($\frac{1}{18}+\frac{1}{24}+\frac{1}{36}$)
⇒ 2(A + B + C) = $\frac{4+3+2}{72}$ = $\frac{9}{72}$ = $\frac{1}{8}$
⇒ (A + B + C) = $\frac{1}{16}$
⇒ A + B + C work together can complete the work in 16 days
Hence, the correct answer is 16 days.
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