Ravi invested ₹P in a scheme A offering simple interest at `10%` pa for two years.He invested the whole amount he received from scheme A in another scheme B offering simple interest at `12%` pa for five years.If the difference between the interests earned from schemes A and B was ₹1300, what is the value of P?

Options

A. 2500
B. 2000
C. 3000
D. 2800

Answer

To solve the problem step by step, we will break down the calculations and reasoning involved in finding the value of \( P \).

### Step 1: Calculate the Simple Interest from Scheme A
The formula for simple interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
For Scheme A:
- Principal \( P \)
- Rate \( R = 10\% \)
- Time \( T = 2 \) years

Substituting these values into the formula gives:
\[ SI_A = \frac{P \times 10 \times 2}{100} = \frac{20P}{100} = \frac{P}{5} \]

### Step 2: Calculate the Total Amount Received from Scheme A
The total amount received from Scheme A after 2 years is:
\[ A_A = P + SI_A = P + \frac{P}{5} = \frac{5P}{5} + \frac{P}{5} = \frac{6P}{5} \]

### Step 3: Calculate the Simple Interest from Scheme B
Now, Ravi invests the total amount from Scheme A into Scheme B. For Scheme B:
- Principal \( = \frac{6P}{5} \)
- Rate \( R = 12\% \)
- Time \( T = 5 \) years

Using the simple interest formula:
\[ SI_B = \frac{\left(\frac{6P}{5}\right) \times 12 \times 5}{100} \]
Calculating this gives:
\[ SI_B = \frac{6P \times 12 \times 5}{5 \times 100} = \frac{72P}{100} = \frac{72P}{100} \]

### Step 4: Set Up the Equation for the Difference in Interest
According to the problem, the difference between the interests earned from Scheme A and Scheme B is ₹1300:
\[ SI_B - SI_A = 1300 \]
Substituting the values we calculated:
\[ \frac{72P}{100} - \frac{P}{5} = 1300 \]

### Step 5: Simplify the Equation
To simplify, convert \( \frac{P}{5} \) to a fraction with a denominator of 100:
\[ \frac{P}{5} = \frac{20P}{100} \]
Now substituting this back into the equation:
\[ \frac{72P}{100} - \frac{20P}{100} = 1300 \]
This simplifies to:
\[ \frac{52P}{100} = 1300 \]

### Step 6: Solve for \( P \)
To find \( P \), multiply both sides by 100:
\[ 52P = 1300 \times 100 \]
\[ 52P = 130000 \]
Now divide both sides by 52:
\[ P = \frac{130000}{52} \]
Calculating this gives:
\[ P = 2500 \]

### Conclusion
The value of \( P \) is ₹2500.