Question : A and B together can finish a work in 30 days. They worked on it for 20 days and then B left. The remaining work was done by A alone in 20 days. In how many days can A alone finish the work?
Option 1: 48 days
Option 2: 50 days
Option 3: 54 days
Option 4: 60 days
Correct Answer: 60 days
Solution :
Let the total work be 1 unit.
A and B together can finish the work in 30 days
The combined work for 1 day = $\frac{1}{30}$ unit.
They worked together for 20 days.
The completed work = $\frac{20}{30}$ = $\frac{2}{3}$ unit.
The remaining work = $(1-\frac{2}{3})=\frac{1}{3}$ unit.
The remaining work was done by A alone in 20 days.
A alone can finish the work = $(20÷\frac{1}{3})$ = (20 × 3) = 60 days.
Hence, the correct answer is 60 days.
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