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
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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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