A, B, and C enter into a partnership. A invests Rs. 3000 at the beginning. B invests 33\frac{1}{3}\% more than A's investment, and C invests the average of A's and B's investments. After 4 months, A withdraws 40\% of his investment, B doubles his investment, and C increases his investment by 20\%. After another 5 months, B leaves the partnership; A doubles his investment, and C keeps his investment unchanged. The total profit at the end of the year is Rs. 677000, which is shared in proportion to their investment and time.

Compare the following:

**Quantity I:** Profit earned by C

**Quantity II:** Average profit earned by A, B, and C together

Which of the following is true?

Question

A, B, and C enter into a partnership. A invests Rs. 3000 at the beginning. B invests 33\frac{1}{3}\% more than A's investment, and C invests the average of A's and B's investments. After 4 months, A withdraws 40\% of his investment, B doubles his investment, and C increases his investment by 20\%. After another 5 months, B leaves the partnership; A doubles his investment, and C keeps his investment unchanged. The total profit at the end of the year is Rs. 677000, which is shared in proportion to their investment and time.

Compare the following:

**Quantity I:** Profit earned by C

**Quantity II:** Average profit earned by A, B, and C together

Which of the following is true?

Accepted Answer

**Solution:**

1. **Initial investments:**
   - A invests Rs. 3000.
   - B invests 33\frac{1}{3}\% more than A, so B's investment = 3000 + \frac{1}{3} 	imes 3000 = Rs. 4000.
   - C invests the average of A and B's investments = \frac{3000 + 4000}{2} = Rs. 3500.

2. **Investment changes after 4 months:**
   - A withdraws 40\%, so remaining investment = 60\% of 3000 = Rs. 1800.
   - B doubles his investment: 2 	imes 4000 = Rs. 8000.
   - C increases investment by 20\%: 3500 + 0.2 	imes 3500 = Rs. 4200.

3. **Investment changes after another 5 months:**
   - B leaves the partnership.
   - A doubles his investment: 2 	imes 1800 = Rs. 3600.
   - C keeps investment unchanged at Rs. 4200.

4. **Calculate the weighted investment (investment 	imes time) for each partner:**
   - A: (3000 	imes 4) + (1800 	imes 5) + (3600 	imes 3) = 12000 + 9000 + 10800 = Rs. 31800
   - B: (4000 	imes 4) + (8000 	imes 5) = 16000 + 40000 = Rs. 56000
   - C: (3500 	imes 4) + (4200 	imes 5) + (4200 	imes 3) = 14000 + 21000 + 12600 = Rs. 47600

5. **Ratio of weighted investments:**
   - A : B : C = 31800 : 56000 : 47600
   - Simplify by dividing by 200: 159 : 280 : 238

6. **Calculate profit share:**
   - Total profit = Rs. 677000
   - Profit of C = \frac{238}{159 + 280 + 238} 	imes 677000 = \frac{238}{677} 	imes 677000 = Rs. 238000

7. **Calculate average profit of A, B, and C:**
   - Average = \frac{677000}{3} \approx Rs. 225666

8. **Comparison:**
   - Profit of C (238000) > Average profit (225666)

**Answer:** (a) Quantity I > Quantity II

Answer

Answer

Answer

Answer