Find the selling price when :
(i) CP = Rs. 1650 and gain = 4%
(ii) CP = Rs. 915 and gain = `6 2/3%`
(iii) CP = Rs.875 and loss = 12%
(iv) CP = Rs.645 and loss = `13 1/3%

Answer

To find the selling price (SP) based on the cost price (CP) and the gain or loss percentage, we can use the following formulas:

1. **For Gain**:
\[ SP = \left( \frac{100 + \text{Gain \%}}{100} \right) \times CP \]

2. **For Loss**:
\[ SP = \left( \frac{100 - \text{Loss \%}}{100} \right) \times CP \]

Now, let's solve each part step by step.

### (i) CP = Rs. 1650 and Gain = 4%

1. **Identify CP and Gain**:
- CP = 1650
- Gain = 4%

2. **Use the formula for SP**:
\[ SP = \left( \frac{100 + 4}{100} \right) \times 1650 \]

3. **Calculate**:
\[ SP = \left( \frac{104}{100} \right) \times 1650 = 1.04 \times 1650 = 1716 \]

**Selling Price = Rs. 1716**

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### (ii) CP = Rs. 915 and Gain = 6 2/3%

1. **Convert Gain to improper fraction**:
- Gain = 6 2/3% = \(\frac{20}{3}\%\)

2. **Identify CP**:
- CP = 915

3. **Use the formula for SP**:
\[ SP = \left( \frac{100 + \frac{20}{3}}{100} \right) \times 915 \]

4. **Calculate**:
- Convert 100 to a fraction with a common denominator:
\[ SP = \left( \frac{300 + 20}{300} \right) \times 915 = \left( \frac{320}{300} \right) \times 915 \]
- Simplify:
\[ SP = \frac{320 \times 915}{300} = \frac{292800}{300} = 976 \]

**Selling Price = Rs. 976**

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### (iii) CP = Rs. 875 and Loss = 12%

1. **Identify CP and Loss**:
- CP = 875
- Loss = 12%

2. **Use the formula for SP**:
\[ SP = \left( \frac{100 - 12}{100} \right) \times 875 \]

3. **Calculate**:
\[ SP = \left( \frac{88}{100} \right) \times 875 = 0.88 \times 875 = 770 \]

**Selling Price = Rs. 770**

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### (iv) CP = Rs. 645 and Loss = 13 1/3%

1. **Convert Loss to improper fraction**:
- Loss = 13 1/3% = \(\frac{40}{3}\%\)

2. **Identify CP**:
- CP = 645

3. **Use the formula for SP**:
\[ SP = \left( \frac{100 - \frac{40}{3}}{100} \right) \times 645 \]

4. **Calculate**:
- Convert 100 to a fraction with a common denominator:
\[ SP = \left( \frac{300 - 40}{300} \right) \times 645 = \left( \frac{260}{300} \right) \times 645 \]
- Simplify:
\[ SP = \frac{260 \times 645}{300} = \frac{167700}{300} = 559 \]

**Selling Price = Rs. 559**

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### Summary of Selling Prices:
1. (i) Rs. 1716
2. (ii) Rs. 976
3. (iii) Rs. 770
4. (iv) Rs. 559

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