The marked price of an article is 60% more than its cost price. What should be the discount (in %) offered by the shopkeeper so that he earns a profit of 12% ?

Options

A. 12
B. 25
C. 30
D. 60

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the Cost Price (CP)
Let's assume the cost price (CP) of the article is \(100\) (in any currency).

**Hint:** Always start by defining a variable for the cost price to simplify calculations.

### Step 2: Calculate the Marked Price (MP)
The marked price (MP) is 60% more than the cost price. Therefore, we can calculate the marked price as follows:
\[ MP = CP + 60\% \text{ of } CP = 100 + 60 = 160 \]

**Hint:** To find a percentage increase, add the percentage to 100% of the original value.

### Step 3: Calculate the Selling Price (SP)
The shopkeeper wants to earn a profit of 12%. Therefore, the selling price (SP) can be calculated as:
\[ SP = CP + 12\% \text{ of } CP = 100 + 12 = 112 \]

**Hint:** To find a percentage profit, add the percentage to 100% of the cost price.

### Step 4: Calculate the Discount
Now, we need to find the discount offered by the shopkeeper. The discount can be calculated using the formula:
\[ \text{Discount} = MP - SP = 160 - 112 = 48 \]

**Hint:** The discount is simply 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:
\[ \text{Discount Percentage} = \left( \frac{\text{Discount}}{MP} \right) \times 100 = \left( \frac{48}{160} \right) \times 100 \]
Calculating this gives:
\[ \text{Discount Percentage} = 30\% \]

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

### Final Answer
The discount that should be offered by the shopkeeper to earn a profit of 12% is **30%**.

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