Question : A and B together complete a work in 20 days, B and C together complete the same work in 30 days, and C and A together complete the same work in 24 days. In how many days A, B, and C together can complete the same work?
Option 1: 8 days
Option 2: 16 days
Option 3: 12 days
Option 4: 15 days
Correct Answer: 16 days
Solution :
Given: A and B can do a piece of work in 20 days. B and C can do it in 30 days, and A and C can do it in 24 days.
We know,
If a man can do the work in $n$ days, then one day's work of the man $=\frac{1}{n}$.
(A + B)'s 1 day's work is $\frac{1}{20}$.
(B + C)'s 1 day's work is $\frac{1}{30}$.
(A + C)'s 1 day's work is $\frac{1}{24}$.
Adding the above three equations we get,
2(A + B + C)'s 1 day's work = $\frac{1}{20}+\frac{1}{30}+\frac{1}{24}=\frac{6+4+5}{120} = \frac{15}{120} = \frac{1}{8}$
⇒ (A + B + C)'s 1 day's work $=\frac{1}{16}$
$\therefore$ (A + B + C) together will complete the work in 16 days.
Hence, the correct answer is 16 days.
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