A borrowed Rs. 8000 from C at a compound interest rate of 20% per annum for 2 years. He lent this amount to B at a certain simple interest rate for 2 years. If the difference between the compound interest paid by A and the simple interest received from B is Rs. 2040, find the rate of interest at which A lent the money to B. (Note: Compound interest paid by A is greater than the simple interest received from B.)

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**Solution:**

1. Calculate the compound interest (CI) paid by A to C:

- Principal, $ P = 8000 $
   - Rate, $ R = 20\% $
   - Time, $ T = 2 $ years

Compound amount after 2 years:
   $$
  $ A = P \times \left(1 + \frac{R}{100}\right)^T = 8000 \times \left(1 + \frac{20}{100}\right)^2 = 8000 \times (1.2)^2 = 8000 \times 1.44 = 11520$
   $$

Compound interest:
   $$
   CI = A - P = 11520 - 8000 = 3520
   $$

2. Let the simple interest (SI) rate at which A lent to B be $ r \% $.

Simple interest for 2 years:
   $$
   SI = \frac{P \times r \times T}{100} = $\frac{8000 \times r \times 2}{100} = 160r$
   $$

3. Given the difference between CI and SI is Rs. 2040, and CI is greater:

$$
   $CI - SI = 2040 \implies 3520 - 160r = 2040$
   $$

4. Solve for $ r $:

$$
   $3520 - 2040 = 160r \implies 1480 = 160r \implies r = \frac{1480}{160} = 9.25\%$
   $$

**Answer:** 9.25\%

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