Question : A and B can complete a work in 36 days and 45 days respectively. They worked together for 2 days and then A left the work. In how many days will B complete the remaining work?
Option 1: 41.5
Option 2: 40
Option 3: 41
Option 4: 40.5
Correct Answer: 40.5
Solution :
The rate at which A works is $\frac{1}{36}$ work per day and the rate at which B works is $\frac{1}{45}$ work per day.
Together, A and B can do $\frac{1}{36} + \frac{1}{45} = \frac{9}{180} = \frac{1}{20}$ work per day.
So, in 2 days, A and B together complete $2 \times \frac{1}{20} = \frac{1}{10}$ of the work.
This means $1 - \frac{1}{10} = \frac{9}{10}$ of the work is left.
Now, only B is working to complete the remaining work.
The time taken by B to complete the remaining work = $\frac{9}{10}÷\frac{1}{45}$ = $\frac{9}{10}\times 45$ = 40.5 days
Hence, the correct answer is 40.5.
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