The simple interest of Rs 2,000 is increased by Rs 40 if the time is increased 4 years. Find the rate of interest.

Options

A. `0.5%`
B. `1.5%`
C. `0.7%`
D. `1.7%`

Answer

To solve the problem step-by-step, we will follow the reasoning outlined in the video transcript.

### Step 1: Understand the problem
We know that the principal amount (P) is Rs 2000. The simple interest (SI) increases by Rs 40 when the time (T) is increased by 4 years. We need to find the rate of interest (R).

**Hint:** Identify the given values: Principal (P), increase in interest (Rs 40), and increase in time (4 years).

### Step 2: Set up the relationship for simple interest
The formula for simple interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]

### Step 3: Calculate the increase in interest
When the time is increased by 4 years, the increase in simple interest is Rs 40. This means:
\[ \text{SI for 4 years} = 40 \]

### Step 4: Find the simple interest for 1 year
Since Rs 40 is the interest for 4 years, we can find the interest for 1 year:
\[ \text{SI for 1 year} = \frac{40}{4} = 10 \]

**Hint:** To find the interest for 1 year, divide the total increase in interest by the number of years.

### Step 5: Set up the equation for 1 year
Now, we can set up the equation for the simple interest for 1 year:
\[ \text{SI for 1 year} = \frac{P \times R \times 1}{100} \]
Substituting the values we have:
\[ 10 = \frac{2000 \times R}{100} \]

### Step 6: Solve for R
Now, we can solve for R:
\[ 10 = \frac{2000R}{100} \]
Multiply both sides by 100:
\[ 1000 = 2000R \]
Now, divide both sides by 2000:
\[ R = \frac{1000}{2000} = 0.5 \]

### Step 7: Conclusion
The rate of interest (R) is 0.5%.

**Hint:** Always check your calculations to ensure accuracy.

### Final Answer
The rate of interest is **0.5%**.