A father had Rs. 1000 and divided it equally between his two sons. One son invested his share at 10\% simple interest for 2 years, while the other son invested his share at 20\% compound interest for 2 years. What is the total interest earned by both sons together?

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**Solution:**

1. The father divides Rs. 1000 equally between two sons, so each son gets:
   $$\frac{1000}{2} = 500 	ext{ Rs.}$$

2. **First son:** invests Rs. 500 at 10\% simple interest for 2 years.
   - Simple Interest (SI) formula: 
     $$SI = \frac{P 	imes R 	imes T}{100}$$
   - Calculate SI:
     $$SI = \frac{500 	imes 10 	imes 2}{100} = 100 	ext{ Rs.}$$

3. **Second son:** invests Rs. 500 at 20\% compound interest for 2 years.
   - Compound Interest (CI) formula:
     $$A = P 	imes \left(1 + \frac{R}{100}ight)^T$$
   - Calculate amount (A):
     $$A = 500 	imes \left(1 + \frac{20}{100}ight)^2 = 500 	imes (1.2)^2 = 500 	imes 1.44 = 720 	ext{ Rs.}$$
   - Compound Interest = Amount - Principal =
     $$720 - 500 = 220 	ext{ Rs.}$$

4. Total interest earned by both sons:
   $$100 + 220 = 320 	ext{ Rs.}$$

**Answer:** Rs. 320

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