A trader marked the price of an article at 25% above the cost price. He allows a certain discount and gains a profit of 12`1/2%`.Find the discount percentage.

Options

A. 0.15
B. 0.125
C. 0.2
D. 0.1

Answer

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

### Step 1: Define the Cost Price
Let the cost price (CP) of the article be \( CP = 100x \).

### Step 2: Calculate the Marked Price
The trader marks the price 25% above the cost price. Therefore, the marked price (MP) can be calculated as:
\[ MP = CP + 25\% \text{ of } CP = 100x + 0.25 \times 100x = 100x + 25x = 125x \]

### Step 3: Calculate the Selling Price
The trader gains a profit of \( 12.5\% \) on the cost price. The selling price (SP) can be calculated as:
\[ SP = CP + 12.5\% \text{ of } CP = 100x + 0.125 \times 100x = 100x + 12.5x = 112.5x \]

### Step 4: Relate Selling Price to Marked Price and Discount
Let the discount percentage be \( d\% \). The selling price can also be expressed in terms of the marked price and the discount:
\[ SP = MP - \text{Discount} \]
\[ \text{Discount} = \frac{d}{100} \times MP \]
Thus, we have:
\[ SP = MP - \frac{d}{100} \times MP \]
\[ SP = MP \left(1 - \frac{d}{100}\right) \]

### Step 5: Substitute Known Values
Now, substituting the values of SP and MP:
\[ 112.5x = 125x \left(1 - \frac{d}{100}\right) \]

### Step 6: Solve for Discount Percentage
Rearranging the equation:
\[ 112.5x = 125x - \frac{125x \cdot d}{100} \]
\[ \frac{125x \cdot d}{100} = 125x - 112.5x \]
\[ \frac{125x \cdot d}{100} = 12.5x \]
Dividing both sides by \( x \) (assuming \( x \neq 0 \)):
\[ \frac{125d}{100} = 12.5 \]
Multiplying both sides by 100:
\[ 125d = 1250 \]
Dividing both sides by 125:
\[ d = 10 \]

### Conclusion
The discount percentage is \( 10\% \).

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