Find the simple interest and amount on each of the following :
(i) Rs. 8400 for 4 years at 8% per annum.
(ii) Rs. 50000 for 3 years `12""1/2%` per annum.
(iii) Rs. 9275 for 2 years at `7""1/2%` per annum.

Answer

Let's solve the question step by step.

### Question:
Find the simple interest and amount on each of the following:
1. Rs. 8400 for 4 years at 8% per annum.
2. Rs. 50000 for 3 years at 12 1/2% per annum.
3. Rs. 9275 for 2 years at 7 1/2% per annum.

### Step-by-Step Solutions:

#### Part (i):
**Given:**
- Principal (P) = Rs. 8400
- Rate (R) = 8% per annum
- Time (T) = 4 years

**Formula for Simple Interest (SI):**
\[ \text{SI} = \frac{P \times R \times T}{100} \]

**Substituting the values:**
\[ \text{SI} = \frac{8400 \times 8 \times 4}{100} \]

**Calculating:**
1. Calculate \( 8400 \times 8 = 67200 \)
2. Then, \( 67200 \times 4 = 268800 \)
3. Finally, \( \frac{268800}{100} = 2688 \)

**Simple Interest = Rs. 2688**

**Amount (A):**
\[ A = P + SI = 8400 + 2688 = 11088 \]

**Amount = Rs. 11088**

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#### Part (ii):
**Given:**
- Principal (P) = Rs. 50000
- Rate (R) = 12 1/2% = \( \frac{25}{2} \)%
- Time (T) = 3 years

**Formula for Simple Interest (SI):**
\[ \text{SI} = \frac{P \times R \times T}{100} \]

**Substituting the values:**
\[ \text{SI} = \frac{50000 \times \frac{25}{2} \times 3}{100} \]

**Calculating:**
1. Calculate \( 50000 \times \frac{25}{2} = 50000 \times 12.5 = 625000 \)
2. Then, \( 625000 \times 3 = 1875000 \)
3. Finally, \( \frac{1875000}{100} = 18750 \)

**Simple Interest = Rs. 18750**

**Amount (A):**
\[ A = P + SI = 50000 + 18750 = 68750 \]

**Amount = Rs. 68750**

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#### Part (iii):
**Given:**
- Principal (P) = Rs. 9275
- Rate (R) = 7 1/2% = \( \frac{15}{2} \)%
- Time (T) = 2 years

**Formula for Simple Interest (SI):**
\[ \text{SI} = \frac{P \times R \times T}{100} \]

**Substituting the values:**
\[ \text{SI} = \frac{9275 \times \frac{15}{2} \times 2}{100} \]

**Calculating:**
1. Calculate \( 9275 \times \frac{15}{2} = 9275 \times 7.5 = 69562.5 \)
2. Then, \( 69562.5 \times 2 = 139125 \)
3. Finally, \( \frac{139125}{100} = 1391.25 \)

**Simple Interest = Rs. 1391.25**

**Amount (A):**
\[ A = P + SI = 9275 + 1391.25 = 10666.25 \]

**Amount = Rs. 10666.25**

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### Summary of Results:
1. For Rs. 8400 at 8% for 4 years:
- Simple Interest = Rs. 2688
- Amount = Rs. 11088

2. For Rs. 50000 at 12 1/2% for 3 years:
- Simple Interest = Rs. 18750
- Amount = Rs. 68750

3. For Rs. 9275 at 7 1/2% for 2 years:
- Simple Interest = Rs. 1391.25
- Amount = Rs. 10666.25

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