A sum of money was put at simple interest at x% p.a. for 3 years Had it been (x+1)% p.a. it would have fetched Rs48 more. The sum (in Rs) is :

Options

A. `1,800`
B. `1,500`
C. `1,750`
D. `1,600`

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Understand the Problem
We need to find the principal amount (P) that was invested at a simple interest rate of x% for 3 years. If the interest rate had been (x + 1)%, the interest earned would have been Rs. 48 more.

### Step 2: Write the Formula for Simple Interest
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest (in percentage)
- \( T \) = Time (in years)

### Step 3: Calculate Simple Interest for Both Cases
1. **Case 1**: Interest at x% for 3 years:
\[ SI_1 = \frac{P \times x \times 3}{100} = \frac{3Px}{100} \]

2. **Case 2**: Interest at (x + 1)% for 3 years:
\[ SI_2 = \frac{P \times (x + 1) \times 3}{100} = \frac{3P(x + 1)}{100} \]

### Step 4: Set Up the Equation Based on the Given Information
According to the problem, the difference in interest between the two cases is Rs. 48:
\[ SI_2 - SI_1 = 48 \]
Substituting the expressions for \( SI_1 \) and \( SI_2 \):
\[ \frac{3P(x + 1)}{100} - \frac{3Px}{100} = 48 \]

### Step 5: Simplify the Equation
Factoring out the common terms:
\[ \frac{3P}{100} \left( (x + 1) - x \right) = 48 \]
This simplifies to:
\[ \frac{3P}{100} \cdot 1 = 48 \]

### Step 6: Solve for Principal (P)
Now, we can solve for \( P \):
\[ \frac{3P}{100} = 48 \]
Multiplying both sides by 100:
\[ 3P = 4800 \]
Dividing by 3:
\[ P = \frac{4800}{3} = 1600 \]

### Final Answer
The sum of money (the principal amount) is Rs. 1600.

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