Question : A and B can finish a work together in 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days can A alone finish the job?
Option 1: 50 days
Option 2: 60 days
Option 3: 48 days
Option 4: 54 days
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Correct Answer: 60 days
Solution :
Let the total work to be done as 1 unit.
Time taken by A and B to finish the work = 30 days
Work done by them in one day = $\frac{1}{30}$ units
Work done by them in 20 days = $20×\frac{1}{30} = \frac{2}{3}$ units
$\therefore$ The remaining work = $1 - \frac{2}{3} = \frac{1}{3}$
Let work done by A in a day = $x$
Work done by him in 20 days = $20x$ units
So, $20x = \frac{1}3$
$⇒x = \frac{1}{60}$
So, A alone can finish the job in $\frac{1}{\frac{1}{60}} = 60$ days
Hence, the correct answer is 60 days.
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