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$\left( a \right)$ 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

Answer
Verified

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.

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