Rinku sells a set of books for Rs 1080, incurring a loss equal to `(1)/(10)` of the cost price. Find the loss per cent and the cost price of the set of books.

Answer

To solve the problem step by step, we will first find the cost price of the set of books and then calculate the loss percentage.

### Step 1: Identify the given values
- Selling Price (SP) = Rs 1080
- Loss = (1/10) of Cost Price (CP)

### Step 2: Express the loss in terms of the cost price
Let the Cost Price (CP) be represented as \( CP \).
According to the problem, the loss can be expressed as:
\[ \text{Loss} = \frac{1}{10} \times CP \]

### Step 3: Use the relationship between cost price, selling price, and loss
The relationship can be expressed as:
\[ CP = SP + \text{Loss} \]
Substituting the values we have:
\[ CP = 1080 + \frac{1}{10} \times CP \]

### Step 4: Rearrange the equation to isolate CP
To isolate \( CP \), we can rearrange the equation:
\[ CP - \frac{1}{10} \times CP = 1080 \]
This can be simplified as:
\[ \frac{10}{10}CP - \frac{1}{10}CP = 1080 \]
\[ \frac{9}{10}CP = 1080 \]

### Step 5: Solve for the cost price
Now, multiply both sides by \( \frac{10}{9} \):
\[ CP = 1080 \times \frac{10}{9} \]
\[ CP = 1200 \]

### Step 6: Calculate the loss
Now that we have the cost price, we can calculate the loss:
\[ \text{Loss} = \frac{1}{10} \times CP = \frac{1}{10} \times 1200 = 120 \]

### Step 7: Calculate the loss percentage
The formula for loss percentage is:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{CP} \right) \times 100 \]
Substituting the values we have:
\[ \text{Loss Percentage} = \left( \frac{120}{1200} \right) \times 100 \]
\[ \text{Loss Percentage} = 10\% \]

### Final Answers:
- Cost Price (CP) = Rs 1200
- Loss Percentage = 10%