P and Q started a business by investing Rs 15000 and Rs $ (15000 + x) $ respectively. After four months, Q withdrew 40\% of his initial investment. At the end of one year, the total profit was Rs 47000, and Q's share of the profit was Rs 22000. Find the value of $ 2x $.

Question

Accepted Answer

**Solution:**

1. Let P's investment be Rs 15000 and Q's initial investment be Rs $15000 + x$.

2. Q withdrew 40\% of his investment after 4 months, so for the first 4 months, Q invested Rs $15000 + x$, and for the remaining 8 months, Q invested only 60\% of $15000 + x$, which is $0.6(15000 + x)$.

3. Calculate the effective investment (capital × time) for both:
   - P's capital for 12 months: $15000 \times 12 = 180000$
   - Q's capital for 4 months: $(15000 + x) \times 4 = 4(15000 + x)$
   - Q's capital for 8 months: $0.6(15000 + x) \times 8 = 4.8(15000 + x)$

4. Total effective investment of Q:
   $$4(15000 + x) + 4.8(15000 + x) = 8.8(15000 + x)$$

5. Ratio of P's to Q's effective investment:
   $$\frac{180000}{8.8(15000 + x)} = \frac{P's\ share}{Q's\ share}$$

6. Given total profit = Rs 47000, and Q's share = Rs 22000, so P's share = Rs 25000.

7. Using the ratio:
   $$\frac{180000}{8.8(15000 + x)} = \frac{25000}{22000} = \frac{25}{22}$$

8. Cross-multiplied:
   $$180000 \times 22 = 25 \times 8.8 (15000 + x)$$

$$3960000 = 220 (15000 + x)$$

9. Divide both sides by 220:
   $$\frac{3960000}{220} = 15000 + x$$

$$18000 = 15000 + x$$

10. Solve for $x$:
    $$x = 18000 - 15000 = 3000$$

11. Find $2x$:
    $$2x = 2 \times 3000 = 6000$$

**Answer:** $6000$

Answer

Answer

Answer

Answer