A shopkeeper has 11 books of same cost price. He sells the first book at certain price, then the sells second book at a price which is Rs 1 less than the selling price of first book and then the sells third book at price which is Rs 1.less than the selling price of second book following this pattern, he sold 11 books. If he sells six books atits cost price. Find the over all percent profit or loss on selling all 11 books.

Options

A. 0.2
B. 0.1
C. `1/11`%
D. No profit/No loss

Answer

To solve the problem step by step, let's break it down clearly:

### Step 1: Define the Cost Price
Let the cost price (CP) of each book be \( x \). Therefore, the total cost price for 11 books is:
\[ \text{Total CP} = 11x \]

### Step 2: Selling Prices of the Books
The selling prices (SP) of the books follow a specific pattern:
- The first book is sold at \( y \) (unknown selling price).
- The second book is sold at \( y - 1 \).
- The third book is sold at \( y - 2 \).
- Continuing this pattern, the selling prices for the books will be:
- 1st book: \( y \)
- 2nd book: \( y - 1 \)
- 3rd book: \( y - 2 \)
- 4th book: \( y - 3 \)
- 5th book: \( y - 4 \)
- 6th book: \( y - 5 \) (sold at cost price, so \( y - 5 = x \))
- 7th book: \( y - 6 \)
- 8th book: \( y - 7 \)
- 9th book: \( y - 8 \)
- 10th book: \( y - 9 \)
- 11th book: \( y - 10 \)

### Step 3: Determine the Value of \( y \)
From the 6th book's selling price:
\[ y - 5 = x \implies y = x + 5 \]

### Step 4: Calculate the Selling Prices
Now we can express the selling prices of all 11 books in terms of \( x \):
- 1st book: \( x + 5 \)
- 2nd book: \( x + 4 \)
- 3rd book: \( x + 3 \)
- 4th book: \( x + 2 \)
- 5th book: \( x + 1 \)
- 6th book: \( x \)
- 7th book: \( x - 1 \)
- 8th book: \( x - 2 \)
- 9th book: \( x - 3 \)
- 10th book: \( x - 4 \)
- 11th book: \( x - 5 \)

### Step 5: Calculate the Total Selling Price (SP)
Now, we sum the selling prices:
\[ \text{Total SP} = (x + 5) + (x + 4) + (x + 3) + (x + 2) + (x + 1) + x + (x - 1) + (x - 2) + (x - 3) + (x - 4) + (x - 5) \]
This simplifies to:
\[ \text{Total SP} = 11x + (5 + 4 + 3 + 2 + 1 - 1 - 2 - 3 - 4 - 5) = 11x + 0 = 11x \]

### Step 6: Calculate Profit or Loss
Now we compare the total selling price with the total cost price:
\[ \text{Total SP} = 11x \quad \text{and} \quad \text{Total CP} = 11x \]
Thus, the overall profit or loss is:
\[ \text{Profit or Loss} = \text{Total SP} - \text{Total CP} = 11x - 11x = 0 \]

### Step 7: Calculate the Percentage of Profit or Loss
Since there is no profit or loss:
\[ \text{Percentage of Profit or Loss} = \left(\frac{\text{Profit or Loss}}{\text{Total CP}}\right) \times 100 = \left(\frac{0}{11x}\right) \times 100 = 0\% \]

### Conclusion
The overall percentage profit or loss on selling all 11 books is **0%**.