To find the sum invested, we need to calculate the individual amounts of simple interest (SI) and compound interest (CI) and use their difference, which is given as ₹197.2.

Let the principal amount be \( P \).

Simple Interest (SI) for 2 years:

The formula for simple interest is:

SI = \( \frac{P \times r \times t}{100} \)

Here, \( r = 10\% \) and \( t = 2 \) years.

Hence,

\( \text{SI} = \frac{P \times 10 \times 2}{100} = \frac{20P}{100} = 0.2P \)

Compound Interest (CI) for 2 years:

The formula for compound interest is:

CI = \( P(1 + \frac{r}{100})^t - P \)

Here, \( r = 10\% \) and \( t = 2 \) years.

Hence,

\( \text{CI} = P(1 + \frac{10}{100})^2 - P = P(1.1)^2 - P \)

Calculating \( (1.1)^2 = 1.21 \), then:

\( \text{CI} = 1.21P - P = 0.21P \)

Difference between CI and SI:

The difference is given as ₹197.2, hence:

\( 0.21P - 0.2P = 197.2 \)

Simplifying:

\( 0.01P = 197.2 \)

Solving for \( P \):

\( P = \frac{197.2}{0.01} = 19720 \)

Therefore, the sum invested is ₹19,720.