An amount of Rs. 12,200 is invested partly in scheme A at 10\% per annum compound interest for 2 years and partly in scheme B at the same rate of 10\% per annum simple interest for 4 years. If the interest earned from both schemes is the same, what is the amount invested in scheme A?

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**Solution:**

1. Let the amount invested in scheme A be $ X $ rupees.

2. Then, the amount invested in scheme B will be $ 12200 - X $ rupees.

3. Calculate the compound interest rate equivalent for 2 years at 10\% per annum:

Compound interest for 2 years = $ 10\% + 10\% + \frac{10\% \times 10\%}{100} = 21\% $

4. Interest from scheme A (compound interest) = $ \frac{21}{100} \times X = 0.21X $

5. Interest from scheme B (simple interest) for 4 years at 10\% per annum = $ \frac{4 \times 10}{100} \times (12200 - X) = 0.4(12200 - X) $

6. Since the interests are equal:

$$ 0.21X = 0.4(12200 - X) $$

7. Simplify the equation:

$$ 0.21X = 4880 - 0.4X $$

$$ 0.21X + 0.4X = 4880 $$

$$ 0.61X = 4880 $$

$$ X = \frac{4880}{0.61} = 8000 $$

**Answer:** Rs. 8000

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