John borrowed Rs. 75000 from his friend and after one year returned Rs. 80000 to his friend. Find the interest.

Answer

To solve the problem step by step, we need to find the simple interest and then the rate of interest.

### Step 1: Identify the principal amount (P) and the total amount returned (A).
- **Principal Amount (P)**: Rs. 75,000 (the amount John borrowed)
- **Total Amount Returned (A)**: Rs. 80,000 (the amount John returned after one year)

### Step 2: Calculate the Simple Interest (SI).
The formula for Simple Interest is:
\[ \text{SI} = A - P \]
Substituting the values:
\[ \text{SI} = 80,000 - 75,000 = 5,000 \]
So, the Simple Interest is Rs. 5,000.

### Step 3: Use the Simple Interest formula to find the Rate of Interest (R).
The formula for Simple Interest is also given by:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- SI = Simple Interest (Rs. 5,000)
- P = Principal Amount (Rs. 75,000)
- R = Rate of Interest (unknown)
- T = Time (1 year)

Substituting the known values into the formula:
\[ 5,000 = \frac{75,000 \times R \times 1}{100} \]

### Step 4: Rearranging the equation to solve for R.
Multiply both sides by 100 to eliminate the fraction:
\[ 5,000 \times 100 = 75,000 \times R \]
\[ 500,000 = 75,000 \times R \]

Now, divide both sides by 75,000 to isolate R:
\[ R = \frac{500,000}{75,000} \]

### Step 5: Simplifying the fraction.
To simplify:
\[ R = \frac{5000}{750} = \frac{5000 \div 250}{750 \div 250} = \frac{20}{3} \]

### Step 6: Convert R to percentage.
Since R is in the form of a fraction, we convert it to a percentage:
\[ R = \frac{20}{3} \% \approx 6.67\% \]

### Final Answer:
- The Simple Interest (SI) is Rs. 5,000.
- The Rate of Interest (R) is approximately \( \frac{20}{3} \% \) or 6.67%.

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