What time taken by sum of rs.7000 to become rs.10500 at the rate of 5% per annum?

Options

A. a. 8years
B. b. 10years
C. c. 5years
D. d. 15years

Answer

To find the time taken for a sum of Rs. 7000 to become Rs. 10500 at the rate of 5% per annum, we can follow these steps:

### Step 1: Identify the Principal and Final Amount
- The principal amount (P) is Rs. 7000.
- The final amount (A) is Rs. 10500.

### Step 2: Calculate the Simple Interest (SI)
- The formula for Simple Interest is:
\[ SI = A - P \]
- Substitute the values:
\[ SI = 10500 - 7000 = 3500 \]

### Step 3: Use the Simple Interest Formula
- 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 (5%)
- \( T \) = Time period (in years)

### Step 4: Substitute Known Values into the Formula
- Substitute \( SI = 3500 \), \( P = 7000 \), and \( R = 5 \):
\[ 3500 = \frac{7000 \times 5 \times T}{100} \]

### Step 5: Rearrange the Equation to Solve for T
- Rearranging gives:
\[ T = \frac{3500 \times 100}{7000 \times 5} \]

### Step 6: Simplify the Equation
- Simplifying the right side:
\[ T = \frac{350000}{35000} = 10 \]

### Step 7: Conclusion
- The time taken for Rs. 7000 to become Rs. 10500 at the rate of 5% per annum is **10 years**.

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