A and B started a business by investing Rs. $X$ and Rs. $X + 1500$ respectively. After 4 months, A withdrew Rs. 1000 from his investment, and B added Rs. 2000 more to his investment. At the end of one year, the ratio of their profits is 23:44. What was the initial amount invested by B?

Question

Accepted Answer

**Solution:**

1. Let the initial investment of A be Rs. $X$. Then, B's initial investment is Rs. $X + 1500$.

2. For the first 4 months:
   - A's investment = $X$
   - B's investment = $X + 1500$

3. After 4 months, A withdraws Rs. 1000, so A's new investment becomes $(X - 1000)$ for the remaining 8 months.

4. B invests Rs. 2000 more after 4 months, so B's new investment becomes $(X + 1500 + 2000) = (X + 3500)$ for the remaining 8 months.

5. Calculate the total investment time product (capital × time) for both:

- A's total contribution:
     $$4 	imes X + 8 	imes (X - 1000) = 4X + 8X - 8000 = 12X - 8000$$

- B's total contribution:
     $$4 	imes (X + 1500) + 8 	imes (X + 3500) = 4X + 6000 + 8X + 28000 = 12X + 34000$$

6. Given the profit ratio is 23:44, so:
   $$\frac{12X - 8000}{12X + 34000} = \frac{23}{44}$$

7. Cross-multiply:
   $$44(12X - 8000) = 23(12X + 34000)$$

$$528X - 352000 = 276X + 782000$$

8. Bring like terms together:
   $$528X - 276X = 782000 + 352000$$

$$252X = 1,134,000$$

9. Solve for $X$:
   $$X = \frac{1,134,000}{252} = 4500$$

10. Initial amount invested by B:
    $$X + 1500 = 4500 + 1500 = 6000$$

**Answer:** Rs. 6000

Answer

Answer

Answer

Answer