Question : A and B together can do a job in 15 days and A alone could do the same job in 20 days. How many days would B take to do half the job if he worked alone?
Option 1: 60
Option 2: 30
Option 3: 45
Option 4: 40
Correct Answer: 30
Solution :
A's job in one day can be expressed as $\frac{1}{20}$ of the total job.
Assume that B completed $\frac{1}{y}$ of the entire job in a single day.
According to the question,
$\frac{1}{20}+\frac{1}{y}=\frac{1}{15}$
⇒ $\frac{1}{y}=\frac{1}{15}-\frac{1}{20}$
⇒ $\frac{1}{y}=\frac{4-3}{60}$
⇒ $\frac{1}{y}=\frac{1}{60}$
⇒ $y=60$
So, B will take 60 days to do the job.
The half job will take $\frac{1}{2} \times60=30$ days to finish.
Hence, the correct answer is 30.
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