A trader marked the selling price of an Article at `20%` above the cost price. At the time of selling he allows certain discount and suffer a loss of `4%` . He allowed the discount of

Options

A. `20%`
B. `25%`
C. `24%`
D. `22%`

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript:

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

**Hint:** Start with a simple value for CP to make calculations easier.

### Step 2: Calculate the Marked Price (MP)
The trader marks the selling price at 20% above the cost price.
So, the marked price (MP) can be calculated as:
\[ MP = CP + (20\% \text{ of } CP) = 100 + (0.20 \times 100) = 100 + 20 = Rs 120 \]

**Hint:** Remember that a percentage increase means adding that percentage of the original amount to itself.

### Step 3: Determine the Selling Price (SP) after Loss
The trader suffers a loss of 4%. The selling price (SP) can be calculated using the formula:
\[ SP = CP - (4\% \text{ of } CP) = 100 - (0.04 \times 100) = 100 - 4 = Rs 96 \]

**Hint:** A loss means you subtract the percentage from the cost price.

### Step 4: Calculate the Discount Allowed
Now, we need to find the discount allowed. The discount can be calculated as:
\[ \text{Discount} = MP - SP = 120 - 96 = Rs 24 \]

**Hint:** The discount is the difference between the marked price and the selling price.

### Step 5: Calculate the Discount Percentage
To find the discount percentage, we use the formula:
\[ \text{Discount Percentage} = \left( \frac{\text{Discount}}{MP} \right) \times 100 = \left( \frac{24}{120} \right) \times 100 \]
Calculating this gives:
\[ \text{Discount Percentage} = \left( \frac{24}{120} \right) \times 100 = 20\% \]

**Hint:** To find the percentage, divide the discount by the marked price and multiply by 100.

### Final Answer
The discount allowed by the trader is **20%**.

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