An amount invested at simple interest gives Rs 2550 interest at rate of 17% per annum in 3 years. What is the principal (in Rs)?

Options

A. a)4000
B. b)5000
C. c)6000
D. d)4500

Answer

To find the principal amount invested at simple interest, we can use the formula for simple interest:

\[ \text{Simple Interest (SI)} = \frac{\text{Principal (P)} \times \text{Rate (R)} \times \text{Time (T)}}{100} \]

Given:
- Simple Interest (SI) = Rs 2550
- Rate (R) = 17% per annum
- Time (T) = 3 years

We need to find the Principal (P).

### Step 1: Substitute the known values into the formula
We can substitute the values of SI, R, and T into the formula:

\[ 2550 = \frac{P \times 17 \times 3}{100} \]

### Step 2: Simplify the equation
Now, simplify the equation:

\[ 2550 = \frac{51P}{100} \]

### Step 3: Multiply both sides by 100
To eliminate the fraction, multiply both sides of the equation by 100:

\[ 2550 \times 100 = 51P \]

\[ 255000 = 51P \]

### Step 4: Divide both sides by 51
Now, to find P, divide both sides by 51:

\[ P = \frac{255000}{51} \]

### Step 5: Calculate the principal
Now, perform the division:

\[ P = 5000 \]

Thus, the principal amount is Rs 5000.

### Final Answer:
The principal amount invested is Rs 5000.

---