A, B, and C invested ₹900, ₹1600, and ₹700 respectively in a business. At the end of the first quarter, they invested additional amounts in the ratio 2 : 5 : 3. At the end of the second quarter, they invested additional amounts in the ratio 4 : 3 : 4. At the end of the third quarter, they invested additional amounts in the ratio 7 : 6 : 7. All investments were kept for one year, and the profit earned is proportional to the investment amount and the duration of investment.

If instead, they had invested additional amounts at the end of each quarter in the same ratio as the first quarter (2 : 5 : 3), what would be B's share of the profit at the end of the year, given the total profit is ₹125000?

Question

A, B, and C invested ₹900, ₹1600, and ₹700 respectively in a business. At the end of the first quarter, they invested additional amounts in the ratio 2 : 5 : 3. At the end of the second quarter, they invested additional amounts in the ratio 4 : 3 : 4. At the end of the third quarter, they invested additional amounts in the ratio 7 : 6 : 7. All investments were kept for one year, and the profit earned is proportional to the investment amount and the duration of investment.

If instead, they had invested additional amounts at the end of each quarter in the same ratio as the first quarter (2 : 5 : 3), what would be B's share of the profit at the end of the year, given the total profit is ₹125000?

Accepted Answer

**Solution:**

1. Initial investments are:
   - A = ₹900
   - B = ₹1600
   - C = ₹700

2. After the first quarter, additional investments are made in the ratio 2 : 5 : 3.

3. The question states that if the additional investments at the end of each quarter were made in the same ratio (2 : 5 : 3), then we need to find B's profit share.

4. Notice that for the first quarter, the sum of A's and C's investments equals B's investment:
   - A + C = 900 + 700 = ₹1600 = B's investment.

5. Since the additional investments are in the same ratio for all quarters, B's total investment over the year will always be equal to the sum of A's and C's investments.

6. Therefore, B's share of the total investment (considering amount and time) is exactly half of the total investment.

7. Profit is divided in proportion to investment and time, so B's profit will be 50% of the total profit.

8. Total profit = ₹125000

9. B's profit = 50% of ₹125000 = ₹62500

**Answer:** ₹62500

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