Question : A and B together can complete a piece of work in 12 days. They worked together for 5 days and then A alone finished the rest of the work in 14 days. A single person can complete the work in:
Option 1: 24 days
Option 2: 22 days
Option 3: 20 days
Option 4: 18 days
Correct Answer: 24 days
Solution :
A and B together can complete the work in 12 days.
They work for 5 days.
So, (12 – 5) = 7 days of work of A + B is left, which is done by A in 14 days.
Let, A alone complete the work in $x$ days.
According to the question,
$\frac{5}{12}+\frac{14}{x} = 1$
$⇒\frac{14}{x} = \frac{7}{12}$
$\therefore x = 24$
Hence, the correct answer is 24 days.
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