A much interest earned on Rs 6000 at rats 4% per annum simple interest in 4 years, in what time that much interest will be on Rs 8000 at rate of 3% per annum?

Options

A. 5 years
B. 6 years
C. 3 years
D. 4 years

Answer

To solve the problem step by step, we will first calculate the simple interest earned on Rs. 6000 at a rate of 4% per annum over 4 years. Then, we will determine how long it will take to earn the same amount of interest on Rs. 8000 at a rate of 3% per annum.

### Step 1: Calculate the Simple Interest on Rs. 6000
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (Rs. 6000)
- \( R \) = Rate of interest (4%)
- \( T \) = Time (4 years)

Substituting the values into the formula:
\[ SI = \frac{6000 \times 4 \times 4}{100} \]
\[ SI = \frac{96000}{100} = 960 \]

### Step 2: Determine the Time for Rs. 8000 at 3% to Earn the Same Interest
Now we need to find out how long it will take for Rs. 8000 to earn the same interest of Rs. 960 at a rate of 3% per annum.

Using the same formula for Simple Interest:
\[ 960 = \frac{8000 \times 3 \times T}{100} \]

### Step 3: Rearranging the Equation to Find Time (T)
Rearranging the equation to solve for \( T \):
\[ 960 = \frac{8000 \times 3 \times T}{100} \]
Multiplying both sides by 100:
\[ 96000 = 8000 \times 3 \times T \]
\[ 96000 = 24000 \times T \]
Now, divide both sides by 24000:
\[ T = \frac{96000}{24000} = 4 \]

### Final Answer
The time required for Rs. 8000 at a rate of 3% per annum to earn the same interest of Rs. 960 is **4 years**.

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