If a merchant offers discount of 25% on the list price, then he makes a loss of 5%. What % Profit or % loss will he make if he sells at a discount of 10% of the list price.

Options

A. 5.5% loss
B. 14% profit
C. 50% profit
D. 26% loss

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the List Price (LP) and Cost Price (CP)
Let the List Price (LP) be represented as \( x \).

### Step 2: Calculate Selling Price (SP) at 25% Discount
When the merchant offers a discount of 25%, the Selling Price (SP) can be calculated as:
\[ SP = LP - (25\% \text{ of } LP) = x - 0.25x = 0.75x \]

### Step 3: Relate Selling Price to Cost Price
According to the problem, when selling at this SP, the merchant incurs a loss of 5%. This means:
\[ SP = CP - (5\% \text{ of } CP) = CP - 0.05CP = 0.95CP \]
Thus, we have:
\[ 0.75x = 0.95CP \]

### Step 4: Express Cost Price in terms of List Price
From the equation \( 0.75x = 0.95CP \), we can express the Cost Price (CP) as:
\[ CP = \frac{0.75x}{0.95} = \frac{75x}{95} = \frac{15x}{19} \]

### Step 5: Calculate Selling Price (SP) at 10% Discount
Now, we need to find the Selling Price when a discount of 10% is offered:
\[ SP = LP - (10\% \text{ of } LP) = x - 0.1x = 0.9x \]

### Step 6: Determine Profit or Loss
Now we will compare this new SP with the CP to find out if there is a profit or loss:
\[ SP = 0.9x \]
We know \( CP = \frac{15x}{19} \).

### Step 7: Calculate Profit or Loss Percentage
To find the profit or loss, we can calculate:
\[ \text{Profit or Loss} = SP - CP = 0.9x - \frac{15x}{19} \]
To simplify this, we need a common denominator:
\[ 0.9x = \frac{0.9 \times 19x}{19} = \frac{17.1x}{19} \]
Now, substituting this back:
\[ \text{Profit or Loss} = \frac{17.1x}{19} - \frac{15x}{19} = \frac{2.1x}{19} \]

### Step 8: Calculate Profit Percentage
Now, we can find the profit percentage:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{\frac{2.1x}{19}}{\frac{15x}{19}} \right) \times 100 \]
This simplifies to:
\[ \text{Profit Percentage} = \left( \frac{2.1}{15} \right) \times 100 = 14\% \]

### Final Answer
The merchant will make a profit of **14%** if he sells at a discount of 10% on the list price.

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