Irshad takes 48 hours to fill one shelf at a store. Rajesh takes half the time to fill a similar shelf. They work together. How much time will they take to fill 15 shelves?

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10 days

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11 days

answer is A.

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Detailed Solution

Let us consider Irshad to be person A and Rajesh be person B.
It is given that the time taken by the person A to fill one shelf is equal to 4848 hours
Also, time taken by the person B to fill one shelf is equal to the half of the time taken by person A
⇒

\frac{48}{2}

⇒24 hours
Now we have to convert into the work done by one hour
Then, the amount of work done by the person A in one hour =

\frac{1}{48}

Also, the amount of work done by the person B in one hour =

\frac{1}{24}

Net Work done = Work done by A + Work done by B
Net Work done =

\frac{1}{48} + \frac{1}{24}

⇒

\frac{1 + 2}{48}

\Rightarrow \frac{3}{48}

∴ Net Work done =

\frac{1}{16}

So, Time taken = reciprocal of work done = 16 hours
Therefore, the time taken by both Irshad and Rajesh to fill one shelf = 16 hours
Similarly, the time taken by both Irshad and Rajesh to fill 15 shelves = 15×16 hours ⇒240 hours
Convert into days.
One day = 24 hours
So 240 hours = 10days.
Hence both the person took to fill the 15 shelve is 10days.

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