At what percentage above the cost price must an article be marked so as to gain 38% after allowing a customer a discount of 8% on the marked price?

Options

A. 48
B. 46
C. 50
D. 45

Answer

To solve the problem of determining the percentage above the cost price at which an article must be marked in order to gain 38% after allowing a customer a discount of 8% on the marked price, we can follow these steps:

### Step 1: Define the Variables
- Let the Cost Price (CP) be 100 (for simplicity).
- Marked Price (MP) is what we need to find.
- Gain (Profit) = 38% of CP = 38% of 100 = 38.
- Discount = 8% of MP.

### Step 2: Set Up the Equation
According to the problem, after giving an 8% discount on the marked price, the selling price (SP) should equal the cost price plus the profit:
\[ SP = CP + Profit \]
\[ SP = 100 + 38 = 138 \]

### Step 3: Express Selling Price in Terms of Marked Price
The selling price can also be expressed in terms of the marked price after applying the discount:
\[ SP = MP - (8\% \text{ of } MP) \]
\[ SP = MP - 0.08 \times MP = 0.92 \times MP \]

### Step 4: Set the Two Expressions for Selling Price Equal
Now, we can set the two expressions for SP equal to each other:
\[ 0.92 \times MP = 138 \]

### Step 5: Solve for Marked Price
To find MP, we rearrange the equation:
\[ MP = \frac{138}{0.92} \]
Calculating this gives:
\[ MP = 150 \]

### Step 6: Calculate the Percentage Above Cost Price
Now we need to find the percentage increase from the cost price to the marked price:
\[ \text{Percentage Increase} = \left( \frac{MP - CP}{CP} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Increase} = \left( \frac{150 - 100}{100} \right) \times 100 \]
\[ \text{Percentage Increase} = \left( \frac{50}{100} \right) \times 100 = 50\% \]

### Final Answer
The article must be marked at **50% above the cost price**.

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