If some amount in rupees at the annual rate of simple interest 5% for six years become Rs. 2600, then the amount is

Options

A. Rs. 1800
B. Rs. 1500
C. Rs. 2000
D. Rs. 2200

Answer

To solve the problem step by step, we will use the formula for simple interest and the relationship between principal, interest, and total amount.

### Step 1: Understand the problem
We need to find the principal amount (let's denote it as \( P \)) that, when invested at a simple interest rate of 5% for 6 years, will amount to Rs. 2600.

### Step 2: Set up the equation
The formula for the total amount \( A \) after \( t \) years at a simple interest rate \( r \) is given by:
\[ A = P + \text{SI} \]
where \( \text{SI} \) (Simple Interest) is calculated as:
\[ \text{SI} = \frac{P \times r \times t}{100} \]
In our case:
- \( A = 2600 \)
- \( r = 5\% \)
- \( t = 6 \)

### Step 3: Substitute the values into the formula
Substituting the values into the formula for simple interest:
\[ \text{SI} = \frac{P \times 5 \times 6}{100} = \frac{30P}{100} = \frac{3P}{10} \]

### Step 4: Write the equation for total amount
Now, we can write the equation for the total amount:
\[ 2600 = P + \frac{3P}{10} \]

### Step 5: Combine like terms
To combine the terms on the right side, we can express \( P \) as \( \frac{10P}{10} \):
\[ 2600 = \frac{10P}{10} + \frac{3P}{10} = \frac{10P + 3P}{10} = \frac{13P}{10} \]

### Step 6: Solve for \( P \)
Now, we can solve for \( P \):
\[ 2600 = \frac{13P}{10} \]
Multiplying both sides by 10 to eliminate the fraction:
\[ 26000 = 13P \]
Now, divide both sides by 13:
\[ P = \frac{26000}{13} = 2000 \]

### Step 7: Conclusion
The principal amount \( P \) is Rs. 2000.