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?
Option 1: 2.34
Option 2: 3.96
Option 3: 2.61
Option 4: 3.69
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Correct Answer: 3.96
Solution :
Let money invests by A and B be $5x$ and $6x$
Total money invests by A in first 4 months = $5x \times 4 = 20x$
Total money invests by B in first 4 months = $6x \times 4 = 24x$
According to the question,
After 4 months money invests by A = $5x \times \frac{4}{5} = 4x$
After 4 months money invest by B = $6x \times (1 + \frac{100}{300})$
= $6x \times\frac{4}{3}$
= $8x$
Total money invests by A in last 8 months = $4x \times 8 = 32x$
Total money invests by B in last 8 months = $8x \times 8 = 64x$
Total money invests by A in a year = $20x + 32x = 52x $
Total money invests by B in a year = $24x + 64x = 88x$
Ratio of money invests by A and B = $52x ∶ 88x$
= 13 ∶ 22
B's profit = $\frac{630000}{35} \times 22$
= 396000
Hence, the correct answer is 3.96 lakhs.
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