A started a business with Rs. 52,000 and after 4 months B joined him with Rs.3

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A started a business with Rs. 52,000 and after 4 months B joined him with Rs.39,000. At the end of the year, out of the total profits B received total Rs. 20,000 including $25 %$ of the profits as commission for managing the business. What amount did A receive?

Answer: Option C
:
C

Profit's share of A and B $= \frac{(52, 000 \times 12)}{(39, 000 \times 8)} = 2 : 1$

Let the profit be Rs. x, then B receives $25 %$ as commission for managing business, the remaining $75 %$ of the total profit x is shared between A and B in the ratio 2:1. Hence B will get ${\frac{1}{3}}^{r d}$ part of this in addition to his commission. Hence his total earning

$= 0.25 x + \frac{1}{3} \times 0.75 x$
$= 0.5 x = 20, 000$
$x = 40, 000$
So,the remaining profit goes to A,hence the profit of A is Rs.20,000.

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