Question

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?

Answer 1

Hint: Here we have to find out the person's work done separately by using the given data. Then we add it to find the work done by the person together in one shelf. Also, we find the time taken by both Irshad and Rajesh to fill $15$. Finally we get the required answer.

Complete step-by-step 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 $48$ hours
Also, time taken by the person B to fill one shelf is equal to the half of the time taken by person A
Here we have to write it as mathematically,
$ \Rightarrow \dfrac{{48}}{2}$
On dividing the terms we get,
$ \Rightarrow 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 = $\dfrac{1}{{48}}$
Also, the amount of work done by the person B in one hour = $\dfrac{1}{{24}}$
Now we have to find out the total amount of work done is,
Net Work done = Work done by A + Work done by B
Net Work done = $\dfrac{1}{{48}} + \dfrac{1}{{24}}$
Taking LCM on both sides we get
$ \Rightarrow \dfrac{{1 + 2}}{{48}}$
On adding the terms and we get,
\[ \Rightarrow \dfrac{3}{{48}}\]
On cancelling the term and we get
$\therefore $ Net Work done =$\dfrac{1}{{16}}$.
Now we conclude that the work done by the person together
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 = $15 \times 16$ hours
Let us multiply the term and we get,
$ \Rightarrow 240$ hours
Here we convert into days.
One day\[ = 24\] hours
So \[240\] hours= $10$days.

Hence both the person took to fill the $15$ shelve is $10$days.

Note: Unitary-method is all about finding value to a single unit.
 If A can complete a work in days, work done by A in \[1\] day is \[\dfrac{1}{n}\]. And if A can complete \[\dfrac{1}{n}\] part of the work in \[1\] day, then A will complete the work in days.