Dev and Deepak start a business in partnership. Dev invested 25\% more capital than Deepak but invested for 4 months less than Deepak. If Deepak's profit share is Rs.4000, which is Rs.1000 more than Dev's share, find the duration (in months) for which Dev invested.

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**Solution:**

1. Let Deepak's capital be *x* and his investment time be *t* months.

2. Dev invests 25\% more capital, so Dev's capital = $1.25x$.

3. Dev invests for 4 months less than Deepak, so Dev's time = $t - 4$ months.

4. Profit share is proportional to the product of capital and time invested.

- Deepak's share ratio = $x 	imes t = xt$
   - Dev's share ratio = $1.25x 	imes (t - 4) = 1.25x(t - 4)$

5. Given Deepak's profit is Rs.4000, which is Rs.1000 more than Dev's, so Dev's profit = Rs.3000.

6. The ratio of their profits equals the ratio of their investments:

$$\frac{4000}{3000} = \frac{xt}{1.25x(t - 4)}$$

7. Simplify the ratio:

$$\frac{4}{3} = \frac{t}{1.25(t - 4)}$$

8. Cross-multiply:

$$4 	imes 1.25 (t - 4) = 3t$$

$$5(t - 4) = 3t$$

$$5t - 20 = 3t$$

$$5t - 3t = 20$$

$$2t = 20$$

$$t = 10$$

9. Dev's investment time = $t - 4 = 10 - 4 = 6$ months.

**Answer:** 6 months

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