The difference between total SI earned on Rs. 'P' at 12% p.a for 3 years and total Ci earned on same sum at 15% p.a for 2 years when compounded annually is Rs. 375. Find P? (in Rs.)

Options

A. 10000
B. 15000
C. 20000
D. 5000

Answer

To solve the problem step by step, we will calculate the Simple Interest (SI) and Compound Interest (CI) and then find the value of P.

### Step 1: Calculate Simple Interest (SI)
The formula for Simple Interest is:

\[ SI = \frac{P \times R \times T}{100} \]

Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

For this problem:
- \( R = 12\% \)
- \( T = 3 \) years

Substituting these values into the formula:

\[ SI = \frac{P \times 12 \times 3}{100} = \frac{36P}{100} = 0.36P \]

### Step 2: Calculate Compound Interest (CI)
The formula for Compound Interest when compounded annually is:

\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]

Where:
- \( R = 15\% \)
- \( T = 2 \) years

First, we calculate the total amount after 2 years:

\[ A = P \left(1 + \frac{15}{100}\right)^2 = P \left(1.15\right)^2 = P \times 1.3225 \]

Now, subtract the principal to find the CI:

\[ CI = A - P = P \times 1.3225 - P = P(1.3225 - 1) = P \times 0.3225 \]

### Step 3: Set up the equation based on the problem statement
According to the problem, the difference between the total SI and total CI is Rs. 375:

\[ SI - CI = 375 \]

Substituting the values we calculated:

\[ 0.36P - 0.3225P = 375 \]

### Step 4: Simplify the equation
Now, simplify the left side:

\[ (0.36 - 0.3225)P = 375 \]

Calculating \( 0.36 - 0.3225 \):

\[ 0.0375P = 375 \]

### Step 5: Solve for P
To find \( P \), divide both sides by 0.0375:

\[ P = \frac{375}{0.0375} \]

Calculating the right side:

\[ P = 10000 \]

### Conclusion
The value of \( P \) is Rs. 10,000.

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