A dealer sold camera for Rs. 1080 gaining `1/8` of its cost price. Find (i) the cost price of camera. And (ii) the gain percent earned by the dealer.

Answer

To solve the given question, we will break it down into two parts as requested:

### Part (i): Finding the Cost Price of the Camera

1. **Let the Cost Price (CP) be \( x \)**:
We denote the cost price of the camera as \( x \).

2. **Determine the Gain**:
The problem states that the dealer gains \( \frac{1}{8} \) of the cost price. Therefore, the gain can be expressed as:
\[ \text{Gain} = \frac{1}{8} \times x \]

3. **Relate Selling Price (SP) to Cost Price and Gain**:
The selling price (SP) is given as Rs. 1080. The relationship between selling price, cost price, and gain is:
\[ \text{SP} = \text{CP} + \text{Gain} \]
Substituting the known values:
\[ 1080 = x + \frac{1}{8}x \]

4. **Combine Like Terms**:
To combine the terms on the right side, we can express \( x \) as \( \frac{8}{8}x \):
\[ 1080 = \frac{8}{8}x + \frac{1}{8}x = \frac{9}{8}x \]

5. **Solve for \( x \)**:
To isolate \( x \), multiply both sides by \( \frac{8}{9} \):
\[ x = 1080 \times \frac{8}{9} \]
\[ x = 960 \]

So, the cost price of the camera is **Rs. 960**.

### Part (ii): Finding the Gain Percent

1. **Calculate the Gain**:
Now that we have the cost price, we can calculate the gain:
\[ \text{Gain} = \frac{1}{8} \times 960 = 120 \]

2. **Calculate Gain Percentage**:
The gain percentage is calculated using the formula:
\[ \text{Gain Percent} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Gain Percent} = \left( \frac{120}{960} \right) \times 100 \]
\[ \text{Gain Percent} = \frac{120}{960} \times 100 = 12.5\% \]

So, the gain percent earned by the dealer is **12.5%**.

### Summary of Solutions:
- (i) Cost Price of the camera: **Rs. 960**
- (ii) Gain Percent earned by the dealer: **12.5%**

---