Question : At the beginning of a partnership business, the capital of B was $\frac{3}{2}$ times that of A. After 8 months B withdrew $\frac{1}{2}$th of his capital and after 10 months A withdrew $\frac{1}{4}$th of his capital. At the end of the year, if the profit incurred is Rs. 53,000, find the amount received by A.
Option 1: Rs. 30,800
Option 2: Rs. 32,000
Option 3: Rs. 30,000
Option 4: Rs. 23,000
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Correct Answer: Rs. 23,000
Solution :
Let A invest Rs. $x$ at the beginning of the partnership business, then the ratio of the profit A and B,
$=(x\times10+\frac{3x}{4}\times2):(\frac{3x}{2}\times8+\frac{3x}{4}\times4)$
$=\frac{23x}{2}:15x$
$=23:30$
The amount received by A in the profit,
$=\frac{23}{53}\times53000$
= Rs. 23,000
Hence, the correct answer is Rs. 23,000.
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