Acharya took a loan of Rs.1,40,000 with simple interest for as many years as the rate of interest. If he paid Rs.68,600 as interest at the end of the loan period, what was the rate of interest?

Options

A. `8%`
B. `6%`
C. `4%`
D. `7%`

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the problem
Acharya took a loan of Rs. 1,40,000 and paid Rs. 68,600 as interest at the end of the loan period. The time (in years) is equal to the rate of interest (in percentage).

### 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:
- \( SI \) = Simple Interest
- \( P \) = Principal amount (loan amount)
- \( R \) = Rate of interest (in %)
- \( T \) = Time (in years)

### Step 3: Substitute the known values
From the problem, we know:
- \( P = 1,40,000 \)
- \( SI = 68,600 \)
- \( T = R \) (since the time is equal to the rate)

Substituting these values into the formula gives:
\[ 68,600 = \frac{1,40,000 \times R \times R}{100} \]

### Step 4: Simplify the equation
Rearranging the equation:
\[ 68,600 = \frac{1,40,000 \times R^2}{100} \]
Multiplying both sides by 100 to eliminate the fraction:
\[ 68,600 \times 100 = 1,40,000 \times R^2 \]
\[ 68,60000 = 1,40,000 \times R^2 \]

### Step 5: Solve for \( R^2 \)
Now, divide both sides by 1,40,000:
\[ R^2 = \frac{68,60000}{1,40,000} \]
Calculating the right side:
\[ R^2 = 49 \]

### Step 6: Find \( R \)
Taking the square root of both sides:
\[ R = \sqrt{49} = 7 \]

### Step 7: Conclusion
The rate of interest is \( 7\% \).