An investor deposited an initial principal of Rs. P in Scheme A at a simple interest rate of 20% per annum for two years. The total maturity amount obtained from Scheme A was then reinvested in Scheme B at a compound interest rate of 10% per annum (compounded annually) for two years. If the difference between the interest earned from Scheme A and Scheme B is Rs. 265, find the value of P.

The correct option is Rs. 2500.

Step 1: Calculate the interest and maturity amount from Scheme A.

Let the initial principal deposited in Scheme A be $P$.

The rate of simple interest is 20% per annum for a time period of 2 years.

The simple interest earned from Scheme A ($I_A$) is calculated as:

$I_A=\frac{P\times ;20\times ;2}{100}=\frac{40P}{100}=0.4P$

The total maturity amount obtained from Scheme A ($A_A$) is:

$A_A=P+I_A=P+0.4P=1.4P$

Step 2: Calculate the interest earned from Scheme B.

The total maturity amount from Scheme A ($1.4P$) is reinvested in Scheme B as the principal ($P_B=1.4P$).

Scheme B offers compound interest at a rate of 10% per annum (compounded annually) for 2 years.

The total maturity amount from Scheme B ($A_B$) is:

$A_B=P_B{\left(1+\frac{10}{100}\right)}^2$

$A_B=1.4P\times ;{\left(1.1\right)}^2=1.4P\times ;1.21=1.694P$

The compound interest earned from Scheme B ($I_B$) is:

$I_B=A_B-P_B=1.694P-1.4P=0.294P$

Step 3: Calculate the value of P using the given difference in interest.

The difference between the interest earned from Scheme A and Scheme B is given as Rs. 265:

$I_A-I_B=265$

$0.4P-0.294P=265$

$0.106P=265$

$P=\frac{265}{0.106}$

$P=2500$

Therefore, the value of $P$ is Rs. 2500.