The simple intrest on a certain sum at 5% per annum for 3 years and 4 years differ by Rs.42.The sum is:

Options

A. Rs. 210
B. Rs 280
C. Rs. 750
D. Rs. 840

Answer

To solve the problem step by step, we will use the formula for simple interest and the information provided in the question.

### Step 1: Understand the Problem
We need to find the principal amount (sum) where the difference in simple interest for 4 years and 3 years at a rate of 5% per annum is Rs. 42.

### 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 %)
- \( T \) = Time (in years)

### Step 3: Set Up the Equation
According to the question, the difference in simple interest for 4 years and 3 years is Rs. 42. This can be expressed as:
\[ SI(4) - SI(3) = 42 \]

Using the formula for simple interest:
\[ \frac{P \times 5 \times 4}{100} - \frac{P \times 5 \times 3}{100} = 42 \]

### Step 4: Simplify the Equation
Now, we can simplify the left side of the equation:
\[ \frac{P \times 5 \times 4 - P \times 5 \times 3}{100} = 42 \]
\[ \frac{P \times 5 (4 - 3)}{100} = 42 \]
\[ \frac{P \times 5}{100} = 42 \]

### Step 5: Solve for Principal (P)
Now, we can solve for \( P \):
\[ P \times 5 = 42 \times 100 \]
\[ P \times 5 = 4200 \]
\[ P = \frac{4200}{5} \]
\[ P = 840 \]

### Conclusion
The principal amount (sum) is Rs. 840.