Find the principal if :
a. the interest is `₹2880` at `8%` p.a. for `3` years.
b. the interest is `₹360` at `5%` p.a. for `4` years.

Answer

To find the principal amount for both parts of the question, we will use the formula for Simple Interest (SI):

\[ SI = \frac{P \times R \times T}{100} \]

Where:
- \( SI \) = Simple Interest
- \( P \) = Principal
- \( R \) = Rate of Interest (per annum)
- \( T \) = Time (in years)

### Part A:
Given:
- Simple Interest (SI) = ₹2880
- Rate of Interest (R) = 8%
- Time (T) = 3 years

1. Substitute the values into the formula:
\[ 2880 = \frac{P \times 8 \times 3}{100} \]

2. Simplify the equation:
\[ 2880 = \frac{24P}{100} \]

3. Multiply both sides by 100 to eliminate the fraction:
\[ 288000 = 24P \]

4. Divide both sides by 24 to solve for P:
\[ P = \frac{288000}{24} \]

5. Calculate the value:
\[ P = 12000 \]

Thus, the principal amount for part A is **₹12000**.

### Part B:
Given:
- Simple Interest (SI) = ₹360
- Rate of Interest (R) = 5%
- Time (T) = 4 years

1. Substitute the values into the formula:
\[ 360 = \frac{P \times 5 \times 4}{100} \]

2. Simplify the equation:
\[ 360 = \frac{20P}{100} \]

3. Multiply both sides by 100 to eliminate the fraction:
\[ 36000 = 20P \]

4. Divide both sides by 20 to solve for P:
\[ P = \frac{36000}{20} \]

5. Calculate the value:
\[ P = 1800 \]

Thus, the principal amount for part B is **₹1800**.

### Summary of Solutions:
- Principal for Part A: ₹12000
- Principal for Part B: ₹1800