Question

A, B, C and D enter into partnership. A subscribes \[\dfrac{1}{3}\] rd of the capital, B subscribes \[\dfrac{1}{4}\] th of the capital, C subscribes \[\dfrac{1}{5}\] th of the capital and D subscribes the rest. How much share did A get in a profit of \[Rs.2460\] .
A. \[Rs.480\]
B. \[Rs.615\]
C. \[Rs.820\]
D. \[Rs.740\]
E.None of these.

Answer 1

Hint: The idea in a partnership-profit problem is that the amount one invests along with the period of his/her investment is proportional to his/her share in the profit. In this problem, we are given the part of the amount that each of the four partners A, B, C and D has contributed to the capital. So, we shall calculate the share of A in profit by using the part(given) of shares contributed by A in the overall capital.

Complete step-by-step answer:
Given that A subscribed \[\dfrac{1}{3}\] rd of the capital. That is, part of or amount of share invested by A is \[\dfrac{1}{3}\] rd of the capital. Therefore, the share of A is \[\dfrac{1}{3}\] rd of the profit.
Given that the overall profit (in Rupees) \[ = Rs.2460\] .
Then, the share of A in the overall profit of \[Rs.2460 = \dfrac{1}{3}of2460\] .
Then, the share of A in the overall profit of \[Rs.2460 = \dfrac{1}{3}(2460)\] .
That is, the share of A in the overall profit of \[Rs.2460 = Rs.820\] .
Therefore, the answer for the given question in (Rupees) is \[Rs.820\] .
So, the correct answer is “Option C”.

Note: As soon as reading the given question one will start calculating the share that D has invested on his part on capital. That is, let the capital be considered having a value as 1. Then, given that
A’s investment in capital \[ = \dfrac{1}{3}\]
B’s investment in capital \[ = \dfrac{1}{4}\]
C’s investment in capital \[ = \dfrac{1}{5}\]
We know that the (Overall) Capital investment is the sum of the investments of A, B, C and D.
Then, D’s investment in capital \[ = 1 - \left[ {\left( {\dfrac{1}{3}} \right) + \left( {\dfrac{1}{4}} \right) + \left( {\dfrac{1}{5}} \right)} \right] = \dfrac{{13}}{{60}}\] .
But these calculations are not necessary to arrive at the required answer.