A sum was invested for 4 yr at a certain rate of simple interest. If it had been invested at 2% more annual rate of interest, then X 56 more would have been obtained. What is the sum?

Options

A. X680
B. X700
C. X720
D. X820

Answer

To solve the problem step by step, we will use the formula for Simple Interest (SI):

**Step 1: Understand the problem and set up the equations.**
We have two scenarios:
1. The first scenario has a certain rate of interest (let's denote it as R%).
2. The second scenario has an interest rate that is 2% more than the first scenario, which is (R + 2)%.

According to the problem, the difference in interest earned from these two scenarios over 4 years is 56.

**Step 2: Write the formula for Simple Interest.**
The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (the sum we want to find)
- \( R \) = Rate of interest
- \( T \) = Time (in years)

**Step 3: Write the equations for both scenarios.**
For the first scenario (interest at R% for 4 years):
\[ \text{SI}_1 = \frac{P \times R \times 4}{100} \]

For the second scenario (interest at (R + 2)% for 4 years):
\[ \text{SI}_2 = \frac{P \times (R + 2) \times 4}{100} \]

**Step 4: Set up the equation based on the difference in interest.**
According to the problem:
\[ \text{SI}_2 - \text{SI}_1 = 56 \]

Substituting the expressions for SI:
\[ \frac{P \times (R + 2) \times 4}{100} - \frac{P \times R \times 4}{100} = 56 \]

**Step 5: Simplify the equation.**
Factor out the common terms:
\[ \frac{P \times 4}{100} \left((R + 2) - R\right) = 56 \]
This simplifies to:
\[ \frac{P \times 4 \times 2}{100} = 56 \]

**Step 6: Solve for P.**
Multiply both sides by 100:
\[ P \times 8 = 5600 \]
Now divide by 8:
\[ P = \frac{5600}{8} = 700 \]

Thus, the sum (or principal) is **700**.

**Final Answer:**
The sum is **700**.

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