The simple interest of Rs 1,000 is increased by Rs 20 if the time is increased by 2 years. Find the rate of interest.

Options

A. 0.02
B. 0.03
C. 0.01
D. 0.04

Answer

To solve the problem step by step, we will use the formula for Simple Interest (SI):

\[ \text{SI} = \frac{P \times R \times T}{100} \]

where:
- \( P \) = Principal amount (initial amount)
- \( R \) = Rate of interest (per annum)
- \( T \) = Time (in years)

### Step 1: Understand the problem
We know that the simple interest increases by Rs 20 when the time is increased by 2 years. This means that the additional interest earned for 2 years is Rs 20.

### Step 2: Calculate the interest for 1 year
If the interest increases by Rs 20 for 2 years, then for 1 year, the increase in interest will be:

\[ \text{Interest for 1 year} = \frac{20}{2} = 10 \text{ Rs} \]

### Step 3: Set up the equation for 1 year
Using the simple interest formula for 1 year, we can express it as:

\[ 10 = \frac{1000 \times R \times 1}{100} \]

### Step 4: Simplify the equation
Now we can simplify the equation:

\[ 10 = \frac{1000R}{100} \]

This simplifies to:

\[ 10 = 10R \]

### Step 5: Solve for R
Now, we can solve for \( R \):

\[ R = \frac{10}{10} = 1 \]

### Step 6: Conclusion
The rate of interest \( R \) is 1%.

### Final Answer
The rate of interest is **1%**.

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