Rajeev and Sanjeev entered into a partnership and invested Rs 36000 and Rs 40000 respectively. After 8 months Rajeev invested an additional capital of Rs 4000. Sanjeev withdrew Rs 4000 after 9 months. At the end of the year total profit was Rs 45800. Find the difference in profits of each

Hint:
Here we need to find the difference in profits of Rajeev and Sanjeev. For that, we will first calculate Rajeev's capital for one year and then we will calculate Sanjeev's capital of one year. Then we will find the profit ratio on the basis of the capitals calculated. From there, we will calculate the profit of each of them and hence we will calculate the difference in profit of each.

Complete step by step solution:
Here, Rajeev’s capital of one year will be equal to the sum of capital of 8 months and 4 months.
Rajeev’s capital of 8 months \[ = {\text{Rs}}36,000 \times 8 = {\text{Rs}}2,88,000\]
Rajeev’s capital of last 4 months \[ = \left( {{\text{Rs}}36,000 + {\text{Rs}}4,000} \right) \times 4 = {\text{Rs}}1,60,000\]
Thus, Rajeev’s capital of 1 year \[ = {\text{Rs}}2,88,000 + {\text{Rs}}1,60,000 = {\text{Rs}}4,48,000\] ………. \[\left( 1 \right)\]
 It is given that Sajeev invested \[Rs{\text{ 40,}}000\] and after 8 months Sanjeev withdrew \[Rs{\text{ }}4000\] after 9 months.
Therefore, Sanjeev’s capital of one year will be equal to the sum of capital of 9 months and 3 months.
Sanjeev’s capital of 9 months \[ = {\text{Rs}}40,000 \times 9 = {\text{Rs}}3,60,000\]
Sanjeev’s capital of last 3 months \[ = \left( {{\text{Rs}}40,000 - {\text{Rs}}4,000} \right) \times 3 = {\text{Rs}}1,08,000\]
Thus, Sanjeev’s capital of 1 year \[ = {\text{Rs}}3,60,000 + {\text{Rs}}1,08,000 = {\text{Rs}}4,68,000\] ……. \[\left( 2 \right)\]
Now, we will calculate the profit ratio which will be calculated on the basis of capitals.
\[{\text{profit ratio}} = \dfrac{{{\text{Rajeev's capital}}}}{{{\text{Sanjeev's capital}}}}\]
Now, we will substitute the value of their capitals in the above equation.
\[ \Rightarrow {\text{profit ratio = }}\dfrac{{{\text{448000}}}}{{{\text{468000}}}}\]
On further simplification, we get
\[ \Rightarrow {\text{profit ratio = }}\dfrac{{{\text{112}}}}{{{\text{117}}}}\]
Now, we will calculate Rajeev’s profit by multiplying the profit ratio with the total profit.
As total profit is equal to Rs 45800, therefore,
Rajeev’s profit \[ = \dfrac{{112}}{{112 + 117}} \times 45800\]
On further simplification, we get
Rajeev’s profit \[ = \dfrac{{112}}{{229}} \times 45800 = {\text{Rs}}22,400\]
Now, we will calculate Sanjeev’s profit by multiplying the profit ratio with the total profit.
As total profit is equal to Rs 45800, therefore,
Sanjeev’s profit \[ = \dfrac{{117}}{{112 + 117}} \times 45800\]
On further simplification, we get
Sanjeev’s profit \[ = \dfrac{{117}}{{229}} \times 45800 = {\text{Rs}}23,400\]

Therefore, difference of their profits is equal to \[{\text{Rs}}23,400 - {\text{Rs}}22,400 = {\text{Rs }}1,000\]

Note:
Here we have calculated the capital of Rajeev and Sanjeev. We need to know about the definition of this term to solve these problems. Capital is defined as the amount that is invested in any business. That’s why we have taken the investment by Rajeev and Sanjeev as their capital. When the return is greater than investment, then there will be profit. If the return is less than the investment, then there is a loss.