The simple interest accrued on an amount of Rs. 2500 at the end of six years is Rs. 1875. What would be the simple interest accrued on an amount of Rs. 6875 at the same rate and same period?

Options

A. A)Rs. 4556.5
B. B)Rs. 5025.25
C. C)Rs. 4895.25
D. D)None of these

Answer

To solve the problem step by step, we will first determine the rate of interest from the given information and then use that rate to calculate the simple interest for the second amount.

### Step 1: Calculate the Rate of Interest
We know the formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(SI\) = Simple Interest
- \(P\) = Principal amount
- \(R\) = Rate of interest per annum
- \(T\) = Time in years

From the question, we have:
- Principal \(P = 2500\)
- Simple Interest \(SI = 1875\)
- Time \(T = 6\) years

Substituting the known values into the formula:
\[ 1875 = \frac{2500 \times R \times 6}{100} \]

### Step 2: Rearranging the Equation
To find \(R\), we can rearrange the equation:
\[ 1875 = \frac{15000R}{100} \]
\[ 1875 = 150R \]

### Step 3: Solve for R
Now, divide both sides by 150:
\[ R = \frac{1875}{150} = 12.5\% \]

### Step 4: Calculate the Simple Interest for Rs. 6875
Now that we have the rate of interest, we can calculate the simple interest for the new principal amount of Rs. 6875 using the same formula:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(P = 6875\)
- \(R = 12.5\%\)
- \(T = 6\) years

Substituting these values into the formula:
\[ SI = \frac{6875 \times 12.5 \times 6}{100} \]

### Step 5: Calculate the Simple Interest
Calculating the above expression:
\[ SI = \frac{6875 \times 12.5 \times 6}{100} = \frac{515625}{100} = 5156.25 \]

### Final Answer
The simple interest accrued on an amount of Rs. 6875 at the same rate and same period is Rs. 5156.25.

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