A sum was put at simple interest at a certain rate for 2yr. If the sum had been put at 3% higher rate, it would have fetched Rs. 72 more. The sum is

Options

A. Rs. 7200
B. Rs. 1200
C. Rs. 300
D. None of these

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Define the variables
Let the principal sum (the amount of money) be denoted as \( x \).

### Step 2: Identify the time period
The time period for which the money is invested is given as 2 years.

### Step 3: Write the formula for simple interest
The formula for calculating simple interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) is the principal amount (which is \( x \)),
- \( R \) is the rate of interest (which we will denote as \( R \)),
- \( T \) is the time period in years (which is 2).

Thus, the simple interest for the original rate \( R \) over 2 years is:
\[ SI = \frac{x \times R \times 2}{100} = \frac{2xR}{100} \]

### Step 4: Calculate the simple interest at a higher rate
If the rate is increased by 3%, the new rate becomes \( R + 3 \). The simple interest at this new rate over the same period of 2 years is:
\[ SI_{new} = \frac{x \times (R + 3) \times 2}{100} = \frac{2x(R + 3)}{100} \]

### Step 5: Set up the equation based on the problem statement
According to the problem, the difference in interest earned when the rate is increased by 3% is Rs. 72. Therefore, we can set up the equation:
\[ SI_{new} - SI = 72 \]
Substituting the expressions for \( SI_{new} \) and \( SI \):
\[ \frac{2x(R + 3)}{100} - \frac{2xR}{100} = 72 \]

### Step 6: Simplify the equation
This simplifies to:
\[ \frac{2x(R + 3 - R)}{100} = 72 \]
\[ \frac{2x \cdot 3}{100} = 72 \]
\[ \frac{6x}{100} = 72 \]

### Step 7: Solve for \( x \)
To isolate \( x \), multiply both sides by 100:
\[ 6x = 7200 \]
Now, divide both sides by 6:
\[ x = \frac{7200}{6} = 1200 \]

### Conclusion
The principal sum is \( \text{Rs. } 1200 \).

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