Question : A and B together can complete a piece of work in 18 days, B and C in 24 days, and A and C in 36 days. In how many days, will all of them together complete the work?
Option 1: 16 days
Option 2: 15 days
Option 3: 12 days
Option 4: 10 days
Correct Answer: 16 days
Solution :
1 day work of A and B = $\frac{1}{18}$ ---------(1)
1 day work of B and C = $\frac{1}{24}$ ---------(2)
1 day work of A and C = $\frac{1}{36}$ ---------(3)
Adding equations (1), (2) and (3), we get:
⇒ 2 × (A + B + C) = $\frac{1}{18}+\frac{1}{24}+\frac{1}{36}$
LCM of (18, 24, 36) = 72
⇒ 2 × (A + B + C)'s 1 day work = $\frac{4+3+2}{72}=\frac{1}{8}$
⇒ (A + B + C)'s 1 day work = $\frac{1}{8×2}=\frac{1}{16}$
So, A, B, and C can work together in 16 days.
Hence, the correct answer is 16 days.
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