A sum was put at simple interest at a certain rate for 2 years. Had it been put at 1% higher rate, it would have fetched 24 more? The sum is

Options

A. 1200
B. 1500
C. 1800
D. 2000

Answer

To solve the problem, we need to find the principal sum (P) that was put at simple interest. Let's break down the solution step by step.

### Step 1: Understand the Simple Interest Formula
The formula for simple interest (SI) is given by:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount (the initial sum of money)
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 2: Set Up the Equations
According to the problem, the sum was put at a certain rate \( R \) for 2 years. The interest earned at this rate is:
\[ SI_1 = \frac{P \times R \times 2}{100} \]

If the rate had been increased by 1% (i.e., \( R + 1 \)), the interest earned would be:
\[ SI_2 = \frac{P \times (R + 1) \times 2}{100} \]

### Step 3: Set Up the Equation Based on the Given Information
According to the problem, the difference between the two interests is 24:
\[ SI_2 - SI_1 = 24 \]

Substituting the expressions for \( SI_1 \) and \( SI_2 \):
\[ \frac{P \times (R + 1) \times 2}{100} - \frac{P \times R \times 2}{100} = 24 \]

### Step 4: Simplify the Equation
Factoring out the common terms:
\[ \frac{2P}{100} \left( (R + 1) - R \right) = 24 \]
This simplifies to:
\[ \frac{2P}{100} \times 1 = 24 \]

### Step 5: Solve for Principal (P)
Now, we can solve for \( P \):
\[ \frac{2P}{100} = 24 \]
Multiplying both sides by 100:
\[ 2P = 2400 \]
Now divide by 2:
\[ P = 1200 \]

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

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