Question : Jeevan can do a piece of work alone in 42 days, while Rishi and Jeevan together can do the same piece of work in 27 days. How many days will Rishi take to complete the same piece of work alone?
Option 1: $74 \frac{3}{5}$
Option 2: $75 \frac{1}{5}$
Option 3: $75 \frac{4}{5}$
Option 4: $75 \frac{3}{5}$
Correct Answer: $75 \frac{3}{5}$
Solution :
Time taken by Jeevan to complete the work = 42 days
Part of work done by Jeevan in a day = $\frac{1}{42}$
Let $x$ be the time taken by Rishi to complete the work.
Part of work done by Rishi in a day = $\frac{1}{x}$
Time taken by Jeevan and Rishi to complete the work = 27 days
Part of work done by Jeevan and Rishi in a day = $\frac{1}{27}$
So, $\frac{1}{42}+\frac{1}{x} =\frac{1}{27}$
⇒ $\frac{1}{x} =\frac{1}{27}-\frac{1}{42}= \frac{14-9}{378} = \frac{5}{378}$
⇒ $x = \frac{378}{5} = 75\frac{3}{5}$
Hence, the correct answer is $75\frac{3}{5}$.
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