Interset earned on `₹12,000` is `₹980` more than the interest earned on `₹8500`. If both the sums were invested at same rate of interest for `4` years, find the rate of interest.

Answer

To find the rate of interest, we will follow these steps:

### Step 1: Identify the given values
- Principal amount 1 (P1) = ₹8500
- Principal amount 2 (P2) = ₹12000
- Time (T) = 4 years
- The interest earned on ₹12000 is ₹980 more than the interest earned on ₹8500.

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

### Step 3: Write the equations for both principal amounts
For principal amount P1 (₹8500):
\[ SI_1 = \frac{8500 \times R \times 4}{100} \]
For principal amount P2 (₹12000):
\[ SI_2 = \frac{12000 \times R \times 4}{100} \]

### Step 4: Set up the equation based on the information given
According to the problem, the interest earned on ₹12000 is ₹980 more than the interest earned on ₹8500:
\[ SI_2 = SI_1 + 980 \]

Substituting the expressions for \(SI_1\) and \(SI_2\):
\[ \frac{12000 \times R \times 4}{100} = \frac{8500 \times R \times 4}{100} + 980 \]

### Step 5: Simplify the equation
We can cancel out the common factors (4/100) from both sides:
\[ 12000R = 8500R + 98000 \]

### Step 6: Rearrange the equation to isolate R
Now, subtract \(8500R\) from both sides:
\[ 12000R - 8500R = 98000 \]
\[ 3500R = 98000 \]

### Step 7: Solve for R
Now, divide both sides by 3500:
\[ R = \frac{98000}{3500} \]
Calculating this gives:
\[ R = 28 \]

### Step 8: Find the rate of interest
To find the percentage, we need to divide by 100:
\[ R = 28 \text{ (as a percentage)} = 7\% \]

### Final Answer
The rate of interest is **7%**.

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