Question : Ramesh does half as much work as Parul in $\frac{4}{5}$ of the time. If together Ramesh and Parul take 24 days to complete the work, then how much time will Parul take to do it?
Option 1: 38 days
Option 2: 41 days
Option 3: 37 days
Option 4: 39 days
Correct Answer: 39 days
Solution :
Let the time taken by Parul to complete the work be $x$.
Part of work done by Parul in a day = $\frac{1}{x}$
Time taken by Ramesh $=2×\frac{4x}{5} = \frac{8x}{5}$
Part of work done by Ramesh in a day = $\frac{5}{8x}$
Time taken by Ramesh and Parul together to complete the work = 24 days
Part of the work done by Ramesh and Parul together in a day = $\frac{1}{24}$
$\frac{1}{x}+\frac{5}{8x}=\frac{1}{24}$
⇒ $\frac{8+5}{8x}=\frac{1}{24}$
⇒ $x = 3 × 13 = 39$ days
Hence, the correct answer is 39 days.
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