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1. 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

Solution:

\begin{aligned} Let the total profit be Rs . x \\ Then, 60 % of the profit \\ = Rs . (\frac{60}{100} \times x) \\ = Rs . \frac{3 x}{5} \end{aligned}

From this part of the profit each gets =

Rs . \frac{3 x}{10}

\begin{aligned} 40 % of total profit \\ = Rs . (\frac{40}{100} \times x) \\ = Rs . \frac{2 x}{5} \end{aligned}

Now, this amount of Rs.

\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} = Rs . (\frac{2 x}{5} \times \frac{25}{42}) \\ =  Rs . \frac{5 x}{21} \end{aligned}

Interest on second capital

\begin{aligned} = Rs . (\frac{2 x}{5} \times \frac{17}{42}) \\ =  Rs . \frac{17 x}{105} \end{aligned}

Total money received by first partner

\begin{aligned} = Rs . (\frac{3 x}{10} + \frac{5 x}{21}) \\ =  Rs . \frac{113 x}{210} \end{aligned}

Total money received by second partner

\begin{aligned} = Rs . (\frac{3 x}{10} + \frac{17 x}{105}) \\ =  Rs . \frac{97 x}{210} \\ ∴ \frac{113 x}{210} - \frac{97 x}{210} = 3000 \\ \Rightarrow x = 39375 \\ Hence, \\ Total profit Rs . 39375 \end{aligned}

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