Question : Prabodh has done $\frac{1}{2}$ of a job in 30 days. Sapan completes the rest of the job in 45 days. In how many days can they together do the job?
Option 1: 18 days
Option 2: 48 days
Option 3: 27 days
Option 4: 36 days
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Correct Answer: 36 days
Solution :
Given: Prabodh has done $\frac{1}{2}$ of a job in $30$ days.
So, he alone will finish the whole work in $60$ days.
Given, Sapan completes half of the work in $45$ days.
So, he will complete the whole work in $90$ days.
In 1 day, work done by both of them together = $\frac{1}{60} + \frac{1}{90} = \frac{5}{180}$
$\therefore$ Number of days to complete the work = $\frac{180}{5 }= 36$ days
Hence, the correct answer is 36 days.
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