A and B entered into a partnership and invested their respective amounts in the ratio of 2:1. C and D entered into another partnership with initial investment ratio of 2:1. The total investment of A and B was 25\% less than that of C and D. If the total profit of all 4 persons at the end of the year is Rs. 10500, then find the profit of A.

Question

Accepted Answer

**Solution:**

1. Let the investments of A and B be in the ratio 2:1, so investments are $2a$ and $a$ respectively.

2. Let the investments of C and D be in the ratio 2:1, so investments are $2b$ and $b$ respectively.

3. Given that total investment of A and B is 25\% less than that of C and D:
   
   $$2a + a = \frac{75}{100} 	imes (2b + b)$$
   
   $$3a = \frac{75}{100} 	imes 3b$$

4. Simplify:
   
   $$3a = \frac{75}{100} 	imes 3b \implies a = \frac{75}{100} b = \frac{3}{4} b$$

5. Let $a = 3x$ and $b = 4x$ for some $x$.

6. Then investments are:
   - A = $2a = 2 	imes 3x = 6x$
   - B = $a = 3x$
   - C = $2b = 2 	imes 4x = 8x$
   - D = $b = 4x$

7. Total investment = $6x + 3x + 8x + 4x = 21x$

8. Profit is shared in the ratio of investments. Total profit = Rs. 10500.

9. Profit of A:
   
   $$\frac{6x}{21x} 	imes 10500 = \frac{6}{21} 	imes 10500 = \frac{2}{7} 	imes 10500 = 3000$$

**Answer:** Rs. 3000

Answer

Answer

Answer