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Q.

Jaya and Seema can together do a piece of work in 10 hours. Seema alone can do it in 15 hours. ____ hours long will Jaya take to do it alone.

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Detailed Solution

Concept- It will take 30 hours for Jaya to complete it alone. We can assume that Jaya will need x hours to finish the job on her own. She will then work one hour more than usual. Seema will work for an hourly rate equal to how long it would take her to finish the task alone.
The sum of Jaya and Seema's individual hourly workloads equals the work completed by both of them in a given hour.

\Rightarrow \frac{1}{x} + \frac{1}{15} = \frac{1}{10}

With

\frac{1}{15}

, we can take both sides out.

\Rightarrow \frac{1}{x} = \frac{1}{10} - \frac{1}{15}

The result of the calculation is

\frac{1}{x} = \frac{3 - 2}{30} = \frac{1}{30} .

The value of x can now be obtained by taking the reciprocal on both sides.

\Rightarrow x = 30

Jaya will therefore need 30 hours to finish the task by herself.
Hence, the correct answer is 30.
ExamType: CBSE

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