### Two partners invested Rs. 125000 and Rs. 85000 respectively in a business. They distribute 60% of the profit equally and decide to distribute the remaining 40% as the interest on their capitals. If one partner received Rs. 3000 more than the other, the total profits is ?

A. Rs. 42250 B. Rs. 39375 C. Rs. 38840 D. Rs. 36575 Answer: Option B
$\begin{array}{l}\text{Let the total profit be Rs.}\ x\\ \text{Then, 60% of the profit}\\ =\text{Rs.}\ \left(\large\frac{60}{100}\times x\right)\\ =\text{Rs.}\ \Large\frac{\text{3x}}{5}\end{array}$ From this part of the profit each gets = Rs.$\Large\frac{3 x}{10}$ $\begin{array}{l} \text{40% of total profit}\\ =\text{Rs.}\ \left(\large\frac{40}{100}\times x\right)\\ =\text{Rs.}\ \Large\frac{\text{2x}}{5}\end{array}$ Now, this amount of Rs.$\Large\frac{2 x}{5}$has been divided in the ratio of capitals, which is 125000 : 85000 or 25 : 17 as interests ∴ Interest on first capital \begin{aligned}&=\text{ Rs. }\left(\frac{2x}{5}\times\frac{25}{42}\right)\\ &=\text{ Rs. }\frac{5x}{21}\end{aligned} Interest on second capital \begin{aligned}&=\text{ Rs. }\left(\frac{2x}{5}\times\frac{17}{42}\right)\\ &=\text{ Rs. }\frac{17x}{105}\end{aligned} Total money received by first partner \begin{aligned}&=\text{ Rs. }\left(\frac{3x}{10}+\frac{5x}{21}\right)\\ &=\text{ Rs. }\frac{113x}{210}\end{aligned} Total money received by second partner \begin{aligned}&=\text{ Rs. }\left(\frac{3x}{10}+\frac{17x}{105}\right)\\ &=\text{ Rs. }\frac{97x}{210}\\ &\therefore\frac{113x}{210}-\frac{97x}{210}=3000\\ &\Rightarrow x=39375\end{aligned} Hence, Total profit Rs.39375