Difference between total Cl and total si on a certain sum at 20% per annum for 2 years is Rs 420. What will be the simple interest earned on same sum at 25% per annum for 3 years?

Options

A. A)Rs 5725
B. B)Rs 7875
C. C)Rs 6525
D. D)Rs 7000

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the given information
We know that the difference between the total Compound Interest (CI) and total Simple Interest (SI) on a certain sum at 20% per annum for 2 years is Rs. 420.

### Step 2: Calculate the Simple Interest (SI) for 2 years
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest
- \( T \) = Time in years

For 2 years at 20%:
\[ SI = \frac{P \times 20 \times 2}{100} = \frac{40P}{100} = 0.4P \]

### Step 3: Calculate the Compound Interest (CI) for 2 years
The formula for Compound Interest is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
For 2 years at 20%:
\[ CI = P \left(1 + \frac{20}{100}\right)^2 - P = P \left(1.2^2\right) - P = P(1.44) - P = 0.44P \]

### Step 4: Set up the equation using the difference between CI and SI
According to the problem:
\[ CI - SI = 420 \]
Substituting the values we found:
\[ 0.44P - 0.4P = 420 \]
\[ 0.04P = 420 \]

### Step 5: Solve for Principal (P)
To find \( P \):
\[ P = \frac{420}{0.04} = 10500 \]

### Step 6: Calculate the Simple Interest (SI) for 3 years at 25%
Now we need to find the Simple Interest for the same principal at 25% for 3 years:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( R = 25\% \)
- \( T = 3 \)

Substituting the values:
\[ SI = \frac{10500 \times 25 \times 3}{100} = \frac{787500}{100} = 7875 \]

### Final Answer
The Simple Interest earned on the same sum at 25% per annum for 3 years is Rs. 7875.

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