Question : A and B can do a work in 8 days and B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in:
Option 1: 4 days
Option 2: 6 days
Option 3: 8 days
Option 4: 12 days
Correct Answer: 8 days
Solution :
Given:
A and B can do a work in 8 days.
⇒ A and B in 1 day can do $\frac{1}{8}$ part of the work
and B and C can do the same work in 12 days.
⇒ B and C in 1 day can do $\frac{1}{12}$ part of the work
Also, A, B, and C together can finish it in 6 days
⇒ A, B and C in 1 day can do $\frac{1}{6}$ part of the work
Now A alone in 1 day can do ($\frac{1}{6}$ — $\frac{1}{12}$) = $\frac{1}{12}$ part of the work
and C alone in 1 day can do ($\frac{1}{6}$ — $\frac{1}{8}$) = $\frac{1}{24}$ part of the work
So A and C together In 1 day can do ($\frac{1}{12}$ + $\frac{1}{24}$) = $\frac{3}{24}$ part of the work
$\therefore$ A and C together will finish it in = (1 ÷ $\frac{3}{24}$) = $\frac{24}{3}$ = 8 days
Hence, the correct answer is 8 days.
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