Gopi invested Rs. X in scheme A at rate of 15% p.a. for two years. The amount received by Gopi from scheme A is reinvest in scheme B at the rate of 10% p.a. for two years on compound interest. If the difference between interest received from A and B is 32.4, then find X?

Let's break down the problem step-by-step to find the value of $X$.

Step 1: Analyze Scheme A
Gopi invested Rs. $X$ in Scheme A at a simple interest rate of 15% per annum for 2 years.
The formula for simple interest (SI) is:
${\text{Interest}}_{\text{A}}=\frac{\text{Principal}\times \text{Rate}\times \text{Time}}{100}$
Substituting the given values:
${\text{Interest}}_{\text{A}}=\frac{X\times 15\times 2}{100}=\frac{30X}{100}=0.3X$

The total amount ($A_{\text{A}}$) received from Scheme A is the sum of the principal and the interest:
$A_{\text{A}}=X+0.3X=1.3X$

Step 2: Analyze Scheme B
The entire amount received from Scheme A ($1.3X$) is reinvested in Scheme B at a rate of 10% per annum for 2 years compounded annually.
The compound interest (CI) rate of 10% for 2 years has an effective interest rate of:
$\text{Effective Rate}=10+10+\frac{10\times 10}{100}=21\%$
Thus, the interest received from Scheme B is 21% of its principal ($1.3X$):
${\text{Interest}}_{\text{B}}=1.3X\times \frac{21}{100}=1.3X\times 0.21=0.273X$

Step 3: Calculate the Difference and Find X
We are given that the difference between the interest received from Scheme A and Scheme B is Rs. 32.4:
${\text{Interest}}_{\text{A}}-{\text{Interest}}_{\text{B}}=32.4$
Substituting the expressions we found:
$0.3X-0.273X=32.4$
$0.027X=32.4$
$X=\frac{32.4}{0.027}$
$X=\frac{32400}{27}=1200$

Therefore, the value of $X$ is 1200 Rs.