Question

Two partners invest Rs \[12,500\] and Rs $ 8500 $ respectively in their business and arrange that \[60\% \] of the profit should be divided equally between them and the remaining profit treated as interest on the capital. If one partner’s share is Rs. \[300\] more than of the other, find the whole amount of the profit.
A.Rs $ 4000 $
B.Rs $ 5000 $
C.Rs $ 3937.50 $
D.Rs $ 2625 $

Answer 1

Hint: It is given that \[60\% \] of the profit is equally distributed between the two and the remaining is distributed according to the share they have given. So, just find the remaining total value, it would automatically lead to a whole amount of profit.

Complete step-by-step answer:
The Amount that the two partners invested Rs \[12,500\] and Rs $ 8500 $ .
Since, the \[60\% \] profit was equally distributed so that we have to find only for the remaining \[40\% \] .
Their ratio =Rs12,500 to Rs8500 = 25:17 $ = \dfrac{{Rs12,500}}{{Rs8500}} = \dfrac{{25}}{{17}} $
The difference in their investment $ = 25 - 17 = 8 $ units.
And Its given that one partners share was Rs \[300\] more than the other that means: $ 8 $ units $ = $ Rs $ 300 $
Therefore, $ 1 $ unit $ = $ Rs $ \dfrac{{300}}{8} $
The difference was $ 8 $ units but the total units invested was $ 25 + 17 = 42 $ units.
Total units ( $ 42 $ units) $ = $ Rs $ \dfrac{{300 \times 42}}{8} = $ $ 1575 $ and this was for \[40\% \] .
Or, \[40\% \] of the profit $ = $ Rs $ \dfrac{{300 \times 42}}{8} = $ $ 1575 $
That implies \[1\% \] of the profit $ = $ Rs $ \dfrac{{1575}}{{40}} $ $ = $ $ 39.375 $
And since, the \[60\% \] of the profit was equally distributed so there would be no change because of that.
So Total profit $ = 100\% $
So, $ 100\% $ of the profit $ = 1\% $ of the profit obtained $ \times 100 = $ Rs $ 39.375 \times 100 = 3937.50 $ .
Therefore, the whole amount of the profit is Rs $ 3937.50 $ .
Hence, the Correct option is Option C i.e Rs $ 3937.50 $ .
So, the correct answer is “Option C”.

Note: There is a probability of misunderstanding the question, so carefully read the question twice before solving.
Don’t start with the whole unit or \[60\% \] of the unit. Start with \[40\% \] for ease in solving the Question.
Take the ratio of investments as units not the invested money.