The difference between simple interset on a certain sum at the rate of 6% per annum for 5 years and 6 years is 25.8. What is the sum (in Rs) ?

Options

A. 480
B. 430
C. 28
D. 516

Answer

To solve the problem step by step, we will use the formula for Simple Interest (SI) and the information provided in the question.

### Step 1: Understand the Problem
We need to find the principal amount (P) given that the difference in simple interest for 5 years and 6 years at a rate of 6% per annum is Rs. 25.8.

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

### Step 3: Calculate Simple Interest for 5 Years and 6 Years
1. For 6 years:
\[ SI_1 = \frac{P \times 6 \times 6}{100} = \frac{36P}{100} \]
2. For 5 years:
\[ SI_2 = \frac{P \times 6 \times 5}{100} = \frac{30P}{100} \]

### Step 4: Find the Difference in Simple Interest
The difference between the simple interest for 6 years and 5 years is given as Rs. 25.8:
\[ SI_1 - SI_2 = 25.8 \]
Substituting the values we found:
\[ \frac{36P}{100} - \frac{30P}{100} = 25.8 \]
This simplifies to:
\[ \frac{(36P - 30P)}{100} = 25.8 \]
\[ \frac{6P}{100} = 25.8 \]

### Step 5: Solve for Principal (P)
To isolate \(P\), multiply both sides by 100:
\[ 6P = 25.8 \times 100 \]
\[ 6P = 2580 \]
Now, divide both sides by 6:
\[ P = \frac{2580}{6} \]
\[ P = 430 \]

### Final Answer
The principal amount (P) is Rs. 430.

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