Manav invested Rs. $X$ in scheme A which offers simple interest at 25\% per annum. After 2 years, he withdraws the entire amount and invests 80\% of it in scheme B, which offers compound interest at 20\% per annum for the next 2 years. If the difference between the interest earned from both schemes is Rs. 700, find the value of $X$.

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**Solution:**

1. Calculate the amount after 2 years in scheme A with simple interest:
   - Simple Interest (SI) = $ $\frac{P \times R \times T}{100} = \frac{X \times 25 \times 2}{100} = \frac{50X}{100} = 0.5X$ $
   - Amount after 2 years = Principal + SI = $ X + 0.5X = 1.5X $

2. Manav invests 80\% of this amount in scheme B:
   - New principal for scheme B = $ $0.8 \times 1.5X = 1.2X $$

3. Calculate compound interest (CI) for 2 years at 20\% per annum on $1.2X$:
   - Amount after 2 years = $ $1.2X \times \left(1 + \frac{20}{100}\right)^2 = 1.2X \times (1.2)^2 = 1.2X \times 1.44 = 1.728X$ $
   - CI = Amount - Principal = $1.728X - 1.2X = 0.528X $

4. Interest from scheme A is $0.5X$, interest from scheme B is $0.528X$.

5. Given the difference between interests is Rs. 700:
   - $$0.528X - 0.5X = 700 \implies 0.028X = 700 $$
   - $$X = \frac{700}{0.028} = 25000$$

**Answer:** Rs. 25000

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