The simple interest accrued on a sum of certain principal is 1200 in 4 year at the rate of 8% per annum. What would be the simple interest accured on thrice of that principal at the rate of 6% per annum in 3 year ?

Options

A. 2025
B. 3025
C. 2250
D. 2150

Answer

To solve the problem step by step, we will follow the given information and apply the formula for simple interest.

### Step 1: Understand the Simple Interest Formula
The formula for calculating simple interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 2: Calculate the Principal Amount
We know that the simple interest accrued on a certain principal is 1200 in 4 years at the rate of 8% per annum. We can use the formula to find the principal \( P \).

Given:
- \( SI = 1200 \)
- \( R = 8\% \)
- \( T = 4 \) years

Plugging these values into the formula:
\[ 1200 = \frac{P \times 8 \times 4}{100} \]

### Step 3: Rearranging the Formula to Find \( P \)
Rearranging the formula to solve for \( P \):
\[ P = \frac{1200 \times 100}{8 \times 4} \]

### Step 4: Calculate the Value of \( P \)
Now, we can calculate \( P \):
\[ P = \frac{1200 \times 100}{32} = \frac{120000}{32} = 3750 \]

### Step 5: Calculate the Simple Interest on Thrice the Principal
Now, we need to calculate the simple interest on thrice the principal at the rate of 6% per annum for 3 years.

Thrice the principal:
\[ 3P = 3 \times 3750 = 11250 \]

Using the simple interest formula again:
\[ SI = \frac{11250 \times 6 \times 3}{100} \]

### Step 6: Calculate the Simple Interest
Calculating the simple interest:
\[ SI = \frac{11250 \times 18}{100} = \frac{202500}{100} = 2025 \]

### Final Answer
The simple interest accrued on thrice the principal at the rate of 6% per annum in 3 years is **2025**.

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