A invested Rs. $X$ in scheme A which offers simple interest at the rate of 12\% per annum for 4 years and receives an interest of Rs. 2160. If Rs. $(X + 500)$ is invested in scheme B which offers compound interest at the rate of 10\% per annum for 2 years, what is the interest received from scheme B?

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**Solution:**

1. Given that the simple interest (SI) on Rs. $X$ at 12\% per annum for 4 years is Rs. 2160.

Using the formula for simple interest:
   $$SI = \frac{P 	imes R 	imes T}{100}$$
   where $P = X$, $R = 12$, and $T = 4$.

Substitute the values:
   $$2160 = \frac{X 	imes 12 	imes 4}{100}$$

2. Simplify to find $X$:
   $$2160 = \frac{48X}{100} \implies 2160 = 0.48X$$
   $$X = \frac{2160}{0.48} = 4500$$

3. Now, the amount invested in scheme B is:
   $$X + 500 = 4500 + 500 = 5000$$

4. Scheme B offers compound interest (CI) at 10\% per annum for 2 years.

The compound interest rate for 2 years can be calculated as:
   $$	ext{Total CI \%} = 10 + 10 + \frac{10 	imes 10}{100} = 21\%$$

5. Calculate the compound interest:
   $$	ext{CI} = 21\% 	ext{ of } 5000 = \frac{21}{100} 	imes 5000 = 1050$$

**Answer:** Rs. 1050

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