What time taken by sum of Rs. 7000 to became 12250 at the rate of 5% per annum?

Options

A. 8 years
B. 10 years
C. 5 years
D. 15 years

Answer

To solve the problem of how long it takes for a sum of Rs. 7000 to become Rs. 12250 at an interest rate of 5% per annum using simple interest, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 7000
- Amount (A) = Rs. 12250
- Rate of interest (R) = 5% per annum

### Step 2: Calculate the Simple Interest (SI)
To find the Simple Interest, we use the formula:
\[ \text{SI} = A - P \]
Substituting the values:
\[ \text{SI} = 12250 - 7000 = 5250 \]

### Step 3: Use the Simple Interest formula to find time (T)
The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
We can rearrange this formula to solve for time (T):
\[ T = \frac{\text{SI} \times 100}{P \times R} \]

### Step 4: Substitute the known values into the formula
Now we substitute the values we have:
\[ T = \frac{5250 \times 100}{7000 \times 5} \]

### Step 5: Simplify the equation
Calculating the denominator:
\[ 7000 \times 5 = 35000 \]
Now substituting this back into the equation:
\[ T = \frac{525000}{35000} \]

### Step 6: Perform the division
Now we can simplify:
\[ T = 15 \]

### Conclusion
The time taken for the sum of Rs. 7000 to become Rs. 12250 at the rate of 5% per annum is **15 years**.

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