A shopkeeper earns a profit of20% on selling a book at 30% discount on list price. How many percentage the list price is greater than cost price.

Options

A. 0.75
B. 0.714
C. 0.8
D. 0.7

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the given information
- The shopkeeper earns a profit of 20% on selling a book.
- The book is sold at a 30% discount on its list price.

### Step 2: Define variables
Let:
- \( CP \) = Cost Price of the book
- \( LP \) = List Price of the book
- Selling Price (SP) can be calculated using the profit percentage.

### Step 3: Calculate the Selling Price (SP)
From the profit percentage:
\[ SP = CP + (20\% \text{ of } CP) = CP \times (1 + 0.20) = 1.20 \times CP \]

### Step 4: Relate Selling Price (SP) to List Price (LP)
Since the book is sold at a 30% discount on the list price:
\[ SP = LP - (30\% \text{ of } LP) = LP \times (1 - 0.30) = 0.70 \times LP \]

### Step 5: Set the two expressions for SP equal to each other
From Steps 3 and 4, we have:
\[ 1.20 \times CP = 0.70 \times LP \]

### Step 6: Solve for the ratio of LP to CP
Rearranging the equation gives:
\[ LP = \frac{1.20 \times CP}{0.70} \]
\[ LP = \frac{1.20}{0.70} \times CP \]
\[ LP = \frac{12}{7} \times CP \]

### Step 7: Calculate how much greater the List Price (LP) is than the Cost Price (CP)
To find out how much greater the list price is than the cost price in percentage:
\[ \text{Percentage Increase} = \left(\frac{LP - CP}{CP}\right) \times 100 \]
Substituting \( LP = \frac{12}{7} \times CP \):
\[ \text{Percentage Increase} = \left(\frac{\frac{12}{7}CP - CP}{CP}\right) \times 100 \]
\[ = \left(\frac{\frac{12}{7}CP - \frac{7}{7}CP}{CP}\right) \times 100 \]
\[ = \left(\frac{\frac{5}{7}CP}{CP}\right) \times 100 \]
\[ = \frac{5}{7} \times 100 \]
\[ = 71.43\% \]

### Final Answer
The list price is approximately **71.43% greater than the cost price**.

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