The marked price of an item is 25% more than its selling price. The selling price of the same item is 20% more than its cost price. The market price of that item is what percentage more than its cost price?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 50%
Let the cost price of the item be C.
According to the problem, the selling price of the item is 20% more than its cost price:
Selling price = Cost price + 20% of cost price
Selling price = C + 0.2C
Selling price = 1.2C
Also, the marked price of the item is 25% more than its selling price:
Marked price = Selling price + 25% of selling price
Marked price = 1.2C + 0.25(1.2C)
Marked price = 1.2C + 0.3C
Marked price = 1.5C
Therefore, the item's marked price is 1.5 times the cost price.
To find the percentage increase in the market price over the cost price, we can use the formula:
Percentage increase = (Increase in value / Original value) × 100%
Here, the increase in value is the difference between the marked price and the cost price:
Increase in value = Marked price - Cost price
Increase in value = 1.5C - C
Increase in value = 0.5C
The original value is the cost price:
Original value = C
Substituting these values in the formula, we get:
Percentage increase = (0.5C / C) × 100%
Percentage increase = 50%