Question

# A, B and C start a business each investing Rs 20000, after 5 months A withdraw Rs 5000, B withdraw Rs 4000 and C invests Rs 6000 more at the end of the year a total profit of Rs 69900 was recorded find the share of each$\left( a \right)$ Rs. 20500, Rs. 27200, Rs. 22200$\left( b \right)$ Rs. 20500, Rs. 25200, Rs. 24200$\left( c \right)$ Rs. 20500, Rs. 21200, Rs. 28200$\left( d \right)$ Rs. 20500, Rs. 23200, Rs. 26200

Hint: In this particular question use the concept of ratio of investment i.e. the ratio of invest of A, B and C is {(A’s initial investment multiplied by 5 months + [A’s initial investment – withdrawal amount] multiplied by the remaining months)} : {(B’s initial investment multiplied by 5 months + [B’s initial investment – withdrawal amount] multiplied by the remaining months)} : {(C’s initial investment multiplied by 5 months + [C’s initial investment + more invested amount] multiplied by the remaining months)}, so use these concepts to reach the solution of the question.

Given data:
A, B and C start a business each investing Rs 20000.
As we all know that in a year there are 12 months.
It is also given that after 5 months A withdraw Rs 5000, B withdraw Rs 4000 and C invests 6000 more.
So the ratio of investment of A, B and C = {(A’s initial investment multiplied by 5 months + [A’s initial investment – withdrawal amount] multiplied by the remaining months)} : {(B’s initial investment multiplied by 5 months + [B’s initial investment – withdrawal amount] multiplied by the remaining months)} : {(C’s initial investment multiplied by 5 months + [C’s initial investment + more invested amount] multiplied by the remaining months)}.
So the ratio of investment of A, B and C = A : B : C = $\left( {20000 \times 5 + \left( {20000 - 5000} \right)7} \right):\left( {20000 \times 5 + \left( {20000 - 4000} \right)7} \right):\left( {20000 \times 5 + \left( {20000 + 6000} \right)7} \right)$
Now simplify we have,
So the ratio of investment of A, B and C = $\left( {205000} \right):\left( {212000} \right):\left( {282000} \right)$
So the ratio of investment of A, B and C = $\left( {205} \right):\left( {212} \right):\left( {282} \right)$
Now it is given that the total profit was Rs. 69900.
So the profit of A is the ratio of investment ratio of A to the sum of the investment ratio of A, B and C multiplied by the profit.
So the profit of A = $\dfrac{{205}}{{205 + 212 + 282}}\left( {69900} \right)$
Now simplify we have,
So the profit of A = $\dfrac{{205}}{{699}}\left( {69900} \right) = 20500$ Rs.
Similarly,
Profit of B = $\dfrac{{212}}{{699}}\left( {69900} \right) = 21200$ Rs.
Profit of C = $\dfrac{{282}}{{699}}\left( {69900} \right) = 28200$ Rs.

So, the correct answer is “Option c”.

Note: Whenever we face such types of questions the key concept we have to remember is that always recall the profit of any particular person is the ratio of investment ratio of the particular person to the sum of the investment ratio of A, B and C multiplied by the profit, so simply substitute the values as above and simplify we will get the required answer.