Question : A and B can complete a task together in 18 hours. After 6 hours, A leaves. B takes 36 hours to finish the rest of the task. How many hours would it have taken A to do the task if he worked alone?
Option 1: 54
Option 2: 45
Option 3: 21
Option 4: 27
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Correct Answer: 27
Solution :
(A + B) can do $\frac{1}{18}$th of the task in 1 hour.
In 6 hours that A and B worked together, they did $\frac{6}{18}=\frac{1}{3}$rd of the task.
What remained after that was $\frac{2}{3}$rd which was done by B alone, in 36 hours.
So, in 36 hours B, alone did $\frac{2}{3}$rd.
$\therefore$ In 1 hour he does $\frac{2}{3}×\frac{1}{36}=\frac{1}{54}$
A alone does $\frac{1}{18}-\frac{1}{54}=\frac{1}{27}$
So, A alone will take 27 hours to do the whole task.
Hence, the correct answer is 27.
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