A man invests an amount of Rs *P* each in two different schemes, A and B. Scheme A offers compound interest at 10% per annum, while scheme B offers compound interest at 20% per annum. Both investments are for a duration of 2 years. If the difference between the compound interest earned from the two schemes is Rs 3105, find the value of *P*.

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**Solution:**

1. Let the principal amount invested in each scheme be Rs *P*.

2. Compound interest formula for 2 years is:
   $$ A = P 	imes \left(1 + \frac{r}{100}ight)^2 $$

3. Calculate the compound interest for scheme A (10% p.a.):
   $$ CI_A = P 	imes \left(1 + \frac{10}{100}ight)^2 - P = P 	imes (1.1)^2 - P = P 	imes (1.21 - 1) = 0.21P $$

4. Calculate the compound interest for scheme B (20% p.a.):
   $$ CI_B = P 	imes \left(1 + \frac{20}{100}ight)^2 - P = P 	imes (1.2)^2 - P = P 	imes (1.44 - 1) = 0.44P $$

5. The difference between the interests is given as Rs 3105:
   $$ CI_B - CI_A = 0.44P - 0.21P = 0.23P = 3105 $$

6. Solve for *P*:
   $$ P = \frac{3105}{0.23} = 13500 $$

**Answer:** Rs 13500

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