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The problem presented in the image is as follows:

**Ram invests the same amount on simple interest and compound interest at a rate of interest 25% and 20% for 4 years and 3 years respectively. He achieved a total interest of Rs.12096. Find the simple interest when he invests the same amount for 2 years at a rate of interest of 22%.**

Let's break this down step by step.

### Let the principal (amount invested) be \( P \).

#### Step 1: Calculate the Simple Interest
- The simple interest formula is \( SI = \frac{P \times R \times T}{100} \).
- For simple interest: Rate \( R = 25\% \) and Time \( T = 4 \) years.
\[
SI_1 = \frac{P \times 25 \times 4}{100} = P
\]
Thus, the simple interest after 4 years is \( P \).

#### Step 2: Calculate the Compound Interest
- The compound interest formula is \( CI = P \left(1 + \frac{R}{100}\right)^T - P \).
- For compound interest: Rate \( R = 20\% \) and Time \( T = 3 \) years.
\[
CI = P \left(1 + \frac{20}{100}\right)^3 - P = P \left(1.2^3\right) - P = P \times 1.728 - P = 0.728P
\]
So, the compound interest is \( 0.728P \).

#### Step 3: Total Interest
The total interest from both investments is given as Rs.12096, so:
\[
P + 0.728P = 12096
\]
\[
1.728P = 12096
\]
\[
P = \frac{12096}{1.728} = 7000
\]
So, the principal \( P = Rs.7000 \).

#### Step 4: Calculate the Simple Interest for the new scenario
Now, Ram invests the same amount \( P = Rs.7000 \) at 22% simple interest for 2 years. Using the simple interest formula:
\[
SI = \frac{P \times R \times T}{100} = \frac{7000 \times 22 \times 2}{100} = 3080
\]
Thus, the simple interest for the new scenario is Rs.3080.

### The correct answer is option 1: **Rs. 3080**.

Would you like further details or have any questions? Here are five related questions you might find interesting:

1. How would the solution change if the rate for compound interest was 15% instead of 20%?
2. What if the investment period for the simple interest was extended to 6 years?
3. How does

Ram invests the same amount on simple interest and compound interest at a rate of interest 25% and 20% for 4 years and 3 years respectively. He achieved a total interest of Rs.12096. Find the simple interest when he invests the same amount for 2 years at a rate of interest of 22%.

Explore how to calculate simple and compound interest for investment scenarios with varying interest rates. This problem demonstrates step-by-step calculations for determining total interest earned and finding the simple interest for future investments. Ideal for high school students preparing for exams.

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