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Ramesh and Naresh are partners in a firm. Their capitals as on $1st$ April, $2017$ were $Rs.50,000$ and $Rs.1,50,000$ respectively. They share profits equally. On $1st$ July, $2017$, they decided that their capitals should be $Rs.2,00,000$ each. The necessary adjustment in the capitals was made by introducing or withdrawing capital. Interest on capital is allowed $@8\% $ p.a. Compute interest on capital for both the partners for the year ended $31st$ March, $2018.$

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Hint: First we will calculate the interest on the old capital for both the partners and then calculate the interest on the new capital then add both of them. We have to use the same formula to find both the results. Finally we get the resultant interest on capital.

Formula used: $Interest = \dfrac{{\Principal \times Rate \times time}}{{100}}$

Complete step-by-step solution:
It is given that the question stated as the capital of Ramesh and Naresh is $Rs.50,000$ and $Rs.1,50,000$ respectively and the interest will be calculated from the period of $1st$ April, $2017$ to $1st$ July,$2017$. Since the period is of $3$ moths the interest on capital will be:
Interested on Ramesh’s capital will be calculated as by using the formula:
$Interest = \dfrac{{50000 \times 8 \times 3}}{{100 \times 12}}$
On simplifying we get:
$Interest = 1000$
Therefore, the interest on Ramesh’s capital initially is $Rs.1000$
Also, we have to find Interested on Naresh’s capital will be calculated as:
$Interest = \dfrac{{150000 \times 8 \times 3}}{{100 \times 12}}$
On simplifying we get:
$Interest = 3000$
Therefore, the interest on Ramesh’s capital initially is $Rs.3000$
Now, the interest on the new capital for both the partners is same which is $Rs.2,00,000$ each.
The interest on the new capital has to be calculated from the period of $1st$ July, $2017$ to $31st$ March, $2018.$
Since the period is of $9$ months, the interest will be calculated as by using the formula and we get:
$Interest = \dfrac{{200000 \times 8 \times 9}}{{100 \times 12}}$
On simplifying we get:
$Interest = 12000$
Therefore, the interest on the new capital of Ramesh and Naresh is $Rs.12000$
Now the total interest on Ramesh’s capital is:
$ \Rightarrow 1000 + 12000$
On simplifying we get:
$ \Rightarrow 13000$, which is the total interest on Ramesh’s capital.
Now the total interest on Naresh’s capital is:
$3000 + 12000$
On simplifying we get:
$ \Rightarrow 15000$, which is the total interest on Naresh’s capital.

Therefore, the total interest in capital for Ramesh is $Rs.13000$ and for Naresh it is $Rs.15000$, which is the required answer.

Note: There are $2$ types of interest calculation which are available which are simple interest and compound interest. Simple interest is when the interest is calculated on the original capital value but during compound interest the interest is calculated on the compound value of the principal and sum of the previous capital.