A sum when reckoned at 6% per annum simple interest amounts to Rs. 4130 in 3 years. Find the sum.

Answer

To solve the problem step by step, we will follow the principles of simple interest.

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

### Step 2: Identify the known values
From the question:
- Amount (A) = Rs. 4130
- Rate (R) = 6% per annum
- Time (T) = 3 years

### Step 3: Calculate the Simple Interest
Using the formula, we can express the Simple Interest in terms of the Principal:
\[ SI = A - P \]
Substituting the values we have:
\[ SI = 4130 - P \]

Now, we can also calculate SI using the formula:
\[ SI = \frac{P \times 6 \times 3}{100} = \frac{18P}{100} \]

### Step 4: Set up the equation
Now we can set the two expressions for Simple Interest equal to each other:
\[ 4130 - P = \frac{18P}{100} \]

### Step 5: Clear the fraction
To eliminate the fraction, multiply the entire equation by 100:
\[ 100(4130 - P) = 18P \]
This simplifies to:
\[ 413000 - 100P = 18P \]

### Step 6: Combine like terms
Now, we will combine the terms involving \(P\):
\[ 413000 = 100P + 18P \]
\[ 413000 = 118P \]

### Step 7: Solve for \(P\)
Now, divide both sides by 118 to find \(P\):
\[ P = \frac{413000}{118} \]
Calculating this gives:
\[ P = 3500 \]

### Conclusion
The sum (Principal) is Rs. 3500.

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