The marked price of an article is 80% more than its cost price. What should be the discount (in %) offered by the shopkeeper so that he earns a profit of 44%?

Options

A. 10
B. 20
C. 30
D. 44

Answer

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

### Step 1: Determine the Cost Price (CP)
Let the Cost Price (CP) of the article be \( x \).

### Step 2: Calculate the Marked Price (MP)
The marked price is 80% more than the cost price. Therefore, we can calculate the marked price as follows:
\[ MP = CP + 80\% \text{ of } CP = x + 0.8x = 1.8x \]

### Step 3: Calculate the Selling Price (SP) for a 44% Profit
The selling price should give a profit of 44% over the cost price. Thus, we can calculate the selling price as:
\[ SP = CP + 44\% \text{ of } CP = x + 0.44x = 1.44x \]

### Step 4: Set up the equation for the discount
We know that the selling price is also equal to the marked price minus the discount. Let the discount be \( d \). Therefore, we can write:
\[ SP = MP - d \]
Substituting the values we have:
\[ 1.44x = 1.8x - d \]

### Step 5: Solve for the discount \( d \)
Rearranging the equation to find \( d \):
\[ d = 1.8x - 1.44x = 0.36x \]

### Step 6: Calculate the discount percentage
The discount percentage can be calculated as follows:
\[ \text{Discount Percentage} = \left( \frac{d}{MP} \right) \times 100 = \left( \frac{0.36x}{1.8x} \right) \times 100 \]
The \( x \) cancels out:
\[ \text{Discount Percentage} = \left( \frac{0.36}{1.8} \right) \times 100 = 20\% \]

### Conclusion
The discount that should be offered by the shopkeeper to earn a profit of 44% is **20%**.

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