To gain 8% after allowing a discount of 10%, by what per cent cost price should be hiked in the list price ?

Options

A. `9%`
B. `11%`
C. `18%`
D. `20%`

Answer

To solve the problem of determining by what percent the cost price should be hiked in the list price to gain 8% after allowing a discount of 10%, we can follow these steps:

### Step 1: Understand the relationship between cost price, list price, discount, and profit.
- Let the cost price (CP) be represented as 100 (for simplicity).
- The list price (LP) is the price before any discount is applied.

### Step 2: Calculate the selling price (SP) after applying the discount.
- Given a discount of 10%, the selling price can be calculated as:
\[ SP = LP - (10\% \text{ of } LP) = LP \times (1 - 0.10) = LP \times 0.90 \]

### Step 3: Calculate the required selling price to achieve an 8% profit.
- To gain an 8% profit on the cost price of 100, the selling price must be:
\[ SP = CP + (8\% \text{ of } CP) = 100 + (0.08 \times 100) = 100 + 8 = 108 \]

### Step 4: Set the two expressions for SP equal to each other.
- From Step 2, we have:
\[ SP = LP \times 0.90 \]
- From Step 3, we have:
\[ SP = 108 \]
- Setting these equal gives:
\[ LP \times 0.90 = 108 \]

### Step 5: Solve for the list price (LP).
- Rearranging the equation:
\[ LP = \frac{108}{0.90} = 120 \]

### Step 6: Determine the increase in cost price.
- The original cost price is 100, and the new list price is 120. The increase in cost price is:
\[ \text{Increase} = LP - CP = 120 - 100 = 20 \]

### Step 7: Calculate the percentage hike in cost price.
- The percentage hike in cost price is calculated as:
\[ \text{Percentage hike} = \left(\frac{\text{Increase}}{CP}\right) \times 100 = \left(\frac{20}{100}\right) \times 100 = 20\% \]

### Final Answer:
The cost price should be hiked by **20%** in the list price.

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