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 BShow Answer
Solution(By Apex Team)
$\begin{array}{l}\text{Let the total profit be Rs.}\ x\\
\text{Then, 60% of the profit}\\
=\text{Rs.}\ \left(\large\frac{60}{100}\times x\right)\\
=\text{Rs.}\ \Large\frac{\text{3x}}{5}\end{array}$
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
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