Question

A dealer allows 30% discount on the marked price of an item and still makes a profit of 10%. By how much percentage is the marked price more than the cost price (rounded off to two places of decimal)?

• A. 45.45%
• B. 26.67%
• C. 57.14%
• D. 33.33%

Answer 1

Answer:

C. 57.14%

The marked price is $57.14\%$ more than the cost price.

1. Find the Relationship Between Marked Price and Cost Price

Let the Cost Price (CP) be $100$.

• Profit percentage: $10\%$

• Selling Price (SP): $100 + 10\% \text{ of } 100 = 110$

The dealer arrives at this Selling Price after offering a $30\%$ discount on the Marked Price (MP):

• $\text{SP} = \text{MP} \times (100\% - 30\%)$

• $110 = \text{MP} \times 0.70$

• $\text{MP} = \frac{110}{0.70} = \frac{1100}{7} \approx 157.14$

2. Calculate the Percentage Markup

Now, find how much higher the Marked Price is compared to the Cost Price:

• $\text{Markup Amount} = \text{MP} - \text{CP} = 157.14 - 100 = 57.14$

• $\text{Markup Percentage} = \frac{57.14}{100} \times 100 = 57.14\%$

Direct Formula Method

You can also solve this quickly using the markup formula:
$\text{Percentage Markup} = \left( \frac{\text{Profit\%} + \text{Discount\%}}{100 - \text{Discount\%}} \right) \times 100$
$\text{Percentage Markup} = \left( \frac{10 + 30}{100 - 30} \right) \times 100 = \frac{40}{70} \times 100 \approx 57.14\%$

Final Answer

The marked price is higher than the cost price by $57.14\%$.