Find the rate of interest if :
a. the interest on `₹1800` for `4` years is `₹432`.
b. the interest on `₹2200` for `3` years is `₹330`.

Answer

To find the rate of interest for the given scenarios, we will use the formula for Simple Interest (SI):

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

Where:
- \( SI \) = Simple Interest
- \( P \) = Principal amount
- \( R \) = Rate of interest (in percentage)
- \( T \) = Time (in years)

### Part (a)

**Step 1: Identify the values.**
- Principal (P) = ₹1800
- Time (T) = 4 years
- Simple Interest (SI) = ₹432

**Step 2: Substitute the values into the formula.**
\[ 432 = \frac{1800 \times R \times 4}{100} \]

**Step 3: Simplify the equation.**
Multiply both sides by 100:
\[ 43200 = 1800 \times R \times 4 \]

**Step 4: Calculate \( 1800 \times 4 \).**
\[ 1800 \times 4 = 7200 \]
So, the equation becomes:
\[ 43200 = 7200 \times R \]

**Step 5: Solve for R.**
Divide both sides by 7200:
\[ R = \frac{43200}{7200} \]
\[ R = 6 \]

**Step 6: Conclusion for Part (a).**
The rate of interest is **6%**.

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### Part (b)

**Step 1: Identify the values.**
- Principal (P) = ₹2200
- Time (T) = 3 years
- Simple Interest (SI) = ₹330

**Step 2: Substitute the values into the formula.**
\[ 330 = \frac{2200 \times R \times 3}{100} \]

**Step 3: Simplify the equation.**
Multiply both sides by 100:
\[ 33000 = 2200 \times R \times 3 \]

**Step 4: Calculate \( 2200 \times 3 \).**
\[ 2200 \times 3 = 6600 \]
So, the equation becomes:
\[ 33000 = 6600 \times R \]

**Step 5: Solve for R.**
Divide both sides by 6600:
\[ R = \frac{33000}{6600} \]
\[ R = 5 \]

**Step 6: Conclusion for Part (b).**
The rate of interest is **5%**.

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