A and B began business with Rs. 3000 and Rs. 4000. After 8 months, A withdraws…

In a partnership where a partner's capital changes during the year, profit is not shared in the simple ratio of the initial capitals -- it is shared in the ratio of each partner's equivalent (time-weighted) capital, found by multiplying the capital invested by the number of months it stayed invested, and summing this across every period of the year.

1. A invests Rs. 3000 for the first 8 months, then withdraws Rs. 1000, leaving Rs. 2000 invested for the remaining 4 months of the year.

2. A's equivalent capital = (3000 x 8) + (2000 x 4) = 24000 + 8000 = 32000.

3. B invests Rs. 4000 for the first 8 months, then advances Rs. 1000 more, taking the investment to Rs. 5000 for the remaining 4 months.

4. B's equivalent capital = (4000 x 8) + (5000 x 4) = 32000 + 20000 = 52000.

5. The profit-sharing ratio of A to B is 32000 : 52000, which simplifies to 8 : 13.

6. A's share of the total profit of Rs. 630 = 630 x 8 / (8 + 13) = 630 x 8 / 21 = Rs. 240.

Cross-check: B's share = 630 x 13 / 21 = Rs. 390, and Rs. 240 + Rs. 390 = Rs. 630, which equals the total profit -- confirming the split is correct.

Therefore, A's share of the profit is Rs. 240.