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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Question : A and B enter into a partnership with capital in the ratio 5: 6. After 4 months, A withdraws $\frac{1}{5}$ of his capital, while B increases his capital by $33 \frac{1}{3} \%$, What is the share (in INR lakhs) of B in the annual profit of INR 6.3 lakhs?
Question : A and B invest in a business in a ratio of 4 : 5. After 10 months, B leaves the business after withdrawing his investment. In the first year, the business made a profit of Rs. 49,000. What is B's share (in Rs.) in this profit?
Question : A and B started a business partnership by investing in a ratio of 3 : 8. C joined them after 4 months with an amount equal to $\frac{3}{4}$th of B. What was their profit (in Rs.) at the end of the year if C got Rs. 24,000 as his share?
Question : A and B together have Rs. 6300. If $\frac{5}{19}$th of A's amount is equal to $\frac{2}{5}$th of B's amount, B's amount is:
Question : Evaluate: $\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}$
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