Question : In a partnership business, B's capital was half of A's. If after 8 months, B withdrew half of his capital and after 2 more months, A withdrew $\frac{1}{4}$th of his capital, then the profit ratio of A to B will be:
Option 1: 5 : 2
Option 2: 10 : 23
Option 3: 2 : 5
Option 4: 23 : 10
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Correct Answer: 23 : 10
Solution : Let $x$ be B's capital. Then, A's capital will be $2x$. Profit ratio of A and B = (capital of A × time period of A) : (capital of B × time period of B) = $(2x × 10 + \frac{3}{4} × 2x×2) : (x × 8 + \frac{x}{2} × 4)$ = $(20x+3x) : (8x+2x)$ = $23x:10x$ = $23:10$ Hence, the correct answer is 23 : 10.
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