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P and Q started a business. The investment of Q is 25% more than that of P. After six months, P doubled his investment and Q withdrew one-third of his investment. If the total profit at the end of a year is ₹12,200, what is the profit share of P?

1. 7200
2. 5000
3. 7800
4. 5600

Correct answer: 7200

Solution

Profit is divided in the ratio of capital-time contributions. P contributes $100\times6 + 200\times6 = 1800$, while Q contributes $125\times6 + \frac{2}{3}\cdot125\times6 = 750 + 500 = 1250$? Correctly, Q's second-half investment is $\frac{2}{3}\cdot125=\frac{250}{3}$, so total contribution is $125\cdot6 + \frac{250}{3}\cdot6 = 750 + 500 = 1250$. Thus ratio $P:Q=1800:1250=36:25$, and P's share is $12200\times\frac{36}{61}=7200$.

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