A sum of ₹2200 is invested at two different at two rates of interest. The difference between the interests got after 4 years is ₹202.40. What is the difference between the rates of interest?

Options

A. 0.033
B. 0.023
C. 0.035
D. 0.025

Explanation

To solve the problem step by step, we will follow the reasoning outlined in the video transcript.

### Step 1: Understand the Problem
We have a principal amount of ₹2200 invested at two different rates of interest (let's call them R1 and R2). The difference in the interest earned from these two investments after 4 years is ₹202.40.

### Step 2: Set Up the Formula for Simple Interest
The formula for calculating simple interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount
- \( R \) = Rate of interest
- \( T \) = Time (in years)

### Step 3: Write the Interest Formulas for Both Investments
For the first investment at rate R1:
\[ SI_1 = \frac{2200 \times R1 \times 4}{100} \]

For the second investment at rate R2:
\[ SI_2 = \frac{2200 \times R2 \times 4}{100} \]

### Step 4: Set Up the Equation for the Difference in Interest
According to the problem, the difference between the two interests is ₹202.40. Therefore, we can write:
\[ SI_1 - SI_2 = 202.40 \]

Substituting the interest formulas into the equation gives:
\[ \frac{2200 \times R1 \times 4}{100} - \frac{2200 \times R2 \times 4}{100} = 202.40 \]

### Step 5: Factor Out Common Terms
We can factor out the common terms from the left side of the equation:
\[ \frac{2200 \times 4}{100} (R1 - R2) = 202.40 \]

### Step 6: Simplify the Expression
Calculating the constant term:
\[ \frac{2200 \times 4}{100} = 88 \]
So, the equation simplifies to:
\[ 88(R1 - R2) = 202.40 \]

### Step 7: Solve for the Difference in Rates
Now, we can isolate \( R1 - R2 \):
\[ R1 - R2 = \frac{202.40}{88} \]

Calculating the right side:
\[ R1 - R2 = 2.3 \]

### Conclusion
The difference between the rates of interest \( R1 \) and \( R2 \) is ₹2.3.

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