For every question, four probable answers as (A), (B), (C) and (D) are given. Only one out of these is correct. Choose the correct answer.
In how many years does the sum of Rs 1,200 become Rs 1,800 at the rate of simple interest of 5% per annum?

Options

A. 10
B. 20
C. 15
D. 25

Answer

To solve the problem of how many years it takes for a sum of Rs 1,200 to become Rs 1,800 at a simple interest rate of 5% per annum, we can follow these steps:

### Step 1: Identify the Principal and Total Amount
- The principal amount (P) is Rs 1,200.
- The total amount (A) after interest is Rs 1,800.

### Step 2: Calculate the Interest Earned
- The interest (I) earned can be calculated as:
\[ I = A - P \]
- Substituting the values:
\[ I = 1800 - 1200 = 600 \]

### Step 3: Use the Simple Interest Formula
- The formula for simple interest is:
\[ I = \frac{P \times R \times T}{100} \]
where:
- \(I\) is the interest,
- \(P\) is the principal,
- \(R\) is the rate of interest per annum,
- \(T\) is the time in years.

### Step 4: Substitute the Known Values
- We know:
- \(I = 600\)
- \(P = 1200\)
- \(R = 5\%\)
- Substitute these values into the formula:
\[ 600 = \frac{1200 \times 5 \times T}{100} \]

### Step 5: Simplify the Equation
- First, simplify the right side:
\[ 600 = \frac{6000 \times T}{100} \]
- This simplifies to:
\[ 600 = 60T \]

### Step 6: Solve for Time (T)
- To find \(T\), divide both sides by 60:
\[ T = \frac{600}{60} = 10 \]

### Conclusion
- The time taken for Rs 1,200 to become Rs 1,800 at a simple interest rate of 5% per annum is **10 years**.

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