Poona invests ₹4200 in Scheme A, which offers `12%` pa simple interest. She also invests ₹(4200 - P) in scheme B offering `10%` pa compound interest, (compounded annually). The difference between the interests Poona earned from both the schemes at the end of 2 years is ₹294. What is the value of P?

Options

A. 1500
B. 800
C. 600
D. 1000

Answer

To solve the problem step by step, we will calculate the simple interest earned from Scheme A and the compound interest earned from Scheme B, and then find the value of P.

### Step 1: Calculate Simple Interest from Scheme A
The formula for simple interest (SI) is given by:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

For Scheme A:
- Principal \( P = 4200 \)
- Rate \( R = 12\% \)
- Time \( T = 2 \) years

Substituting the values:
\[ SI_A = \frac{4200 \times 12 \times 2}{100} = \frac{4200 \times 24}{100} = \frac{100800}{100} = 1008 \]

### Step 2: Calculate Compound Interest from Scheme B
The formula for compound interest (CI) is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

For Scheme B:
- Principal \( P = 4200 - P \)
- Rate \( R = 10\% \)
- Time \( T = 2 \) years

Substituting the values:
\[ CI_B = (4200 - P) \left(1 + \frac{10}{100}\right)^2 - (4200 - P) \]
\[ = (4200 - P) \left(1.1\right)^2 - (4200 - P) \]
\[ = (4200 - P) \times 1.21 - (4200 - P) \]
\[ = (4200 - P) \times 1.21 - (4200 - P) \]
\[ = (4200 - P) \times (1.21 - 1) = (4200 - P) \times 0.21 \]

### Step 3: Set Up the Equation
According to the problem, the difference between the simple interest from Scheme A and the compound interest from Scheme B is ₹294:
\[ SI_A - CI_B = 294 \]
Substituting the values we calculated:
\[ 1008 - 0.21(4200 - P) = 294 \]

### Step 4: Solve for P
Rearranging the equation:
\[ 1008 - 294 = 0.21(4200 - P) \]
\[ 714 = 0.21(4200 - P) \]

Now, divide both sides by 0.21:
\[ 4200 - P = \frac{714}{0.21} \]
Calculating the right side:
\[ 4200 - P = 3400 \]

Now, solving for P:
\[ P = 4200 - 3400 = 800 \]

### Final Answer
The value of \( P \) is ₹800.

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