After giving `20%` discount on an article a shopkeeper earns `30%` profit Marked price is what percent of cost price ?

Options

A. A)`137.5%`
B. B)`162.5%`
C. C)`122.5%`
D. D)`150%`

Answer

To solve the problem step by step, we will determine the relationship between the cost price, selling price, and marked price based on the given discounts and profit percentages.

### Step 1: Define the Cost Price
Let the cost price (CP) be 100. This simplifies our calculations.

**Hint:** Start with a base value for the cost price to make calculations easier.

### Step 2: Calculate the Selling Price
Since the shopkeeper earns a 30% profit on the cost price, we can calculate the selling price (SP) as follows:
\[ SP = CP + (30\% \text{ of } CP) = 100 + 30 = 130 \]

**Hint:** Profit is calculated as a percentage of the cost price, so add the profit to the cost price to find the selling price.

### Step 3: Understand the Discount
The shopkeeper gives a 20% discount on the marked price (MP). This means that the selling price is 80% of the marked price (since 100% - 20% = 80%).

**Hint:** Remember that a discount reduces the marked price to a percentage of itself.

### Step 4: Set Up the Equation for Marked Price
We can express the relationship between the selling price and the marked price as:
\[ SP = 80\% \text{ of } MP \]
This can be written as:
\[ 130 = 0.8 \times MP \]

**Hint:** Use the percentage to express the selling price in terms of the marked price.

### Step 5: Solve for Marked Price
To find the marked price, rearrange the equation:
\[ MP = \frac{130}{0.8} = 162.5 \]

**Hint:** Dividing the selling price by the percentage (in decimal form) gives you the marked price.

### Step 6: Calculate Marked Price as a Percentage of Cost Price
Now, we need to find out what percentage the marked price is of the cost price:
\[ \text{Percentage of CP} = \left( \frac{MP}{CP} \right) \times 100 = \left( \frac{162.5}{100} \right) \times 100 = 162.5\% \]

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

### Conclusion
The marked price is **162.5%** of the cost price.

**Final Answer:** The marked price is 162.5% of the cost price.