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A shopkeeper wants to earn a profit of 20% and at the same time, the minimum discount which he wants to offer is 25%. What should be the minimum percentage mark-up over CP?
- a)60%
- b)42.5%
- c)62.5%
- d)35%
Correct answer is option 'A'. Can you explain this answer?
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To find the minimum percentage mark-up over the cost price (CP), we need to consider both the desired profit margin and the minimum discount offered by the shopkeeper. Let's break down the solution into steps:
Step 1: Understand the given information
The shopkeeper wants to earn a profit of 20% and offer a minimum discount of 25%.
Step 2: Calculate the selling price (SP) after the discount
Let's assume the cost price (CP) of the item is 100.
Discount = 25% of CP = 25% of 100 = 25
SP = CP - Discount = 100 - 25 = 75
Step 3: Calculate the mark-up over CP
Mark-up is the amount added to the cost price to determine the selling price. In this case, the mark-up is the difference between the selling price after the discount and the cost price.
Mark-up = SP - CP = 75 - 100 = -25
Step 4: Calculate the minimum percentage mark-up over CP
To calculate the minimum percentage mark-up over CP, we need to find the percentage of the mark-up in relation to the CP.
Percentage mark-up over CP = (Mark-up / CP) * 100
Substituting the values, we get:
Percentage mark-up over CP = (-25 / 100) * 100 = -25%
Step 5: Adjust the mark-up to achieve the desired profit margin
Since the calculated mark-up is negative, it means the selling price is lower than the cost price. To achieve a profit margin of 20%, the mark-up needs to be positive. We can adjust the mark-up by adding the desired profit margin to it.
Adjusted mark-up = Mark-up + Desired profit margin
Substituting the values, we get:
Adjusted mark-up = -25 + 20 = -5
Step 6: Calculate the minimum percentage mark-up over CP after adjusting for the profit margin
Percentage mark-up over CP = (Adjusted mark-up / CP) * 100
Substituting the values, we get:
Percentage mark-up over CP = (-5 / 100) * 100 = -5%
The calculated mark-up after adjusting for the profit margin is still negative. This means that the shopkeeper cannot achieve both the desired profit margin of 20% and the minimum discount of 25% simultaneously.
Therefore, the correct option is A) 60%, which suggests that the shopkeeper needs to mark up the price by at least 60% over the cost price to achieve the desired profit margin and offer the minimum discount.
Step 1: Understand the given information
The shopkeeper wants to earn a profit of 20% and offer a minimum discount of 25%.
Step 2: Calculate the selling price (SP) after the discount
Let's assume the cost price (CP) of the item is 100.
Discount = 25% of CP = 25% of 100 = 25
SP = CP - Discount = 100 - 25 = 75
Step 3: Calculate the mark-up over CP
Mark-up is the amount added to the cost price to determine the selling price. In this case, the mark-up is the difference between the selling price after the discount and the cost price.
Mark-up = SP - CP = 75 - 100 = -25
Step 4: Calculate the minimum percentage mark-up over CP
To calculate the minimum percentage mark-up over CP, we need to find the percentage of the mark-up in relation to the CP.
Percentage mark-up over CP = (Mark-up / CP) * 100
Substituting the values, we get:
Percentage mark-up over CP = (-25 / 100) * 100 = -25%
Step 5: Adjust the mark-up to achieve the desired profit margin
Since the calculated mark-up is negative, it means the selling price is lower than the cost price. To achieve a profit margin of 20%, the mark-up needs to be positive. We can adjust the mark-up by adding the desired profit margin to it.
Adjusted mark-up = Mark-up + Desired profit margin
Substituting the values, we get:
Adjusted mark-up = -25 + 20 = -5
Step 6: Calculate the minimum percentage mark-up over CP after adjusting for the profit margin
Percentage mark-up over CP = (Adjusted mark-up / CP) * 100
Substituting the values, we get:
Percentage mark-up over CP = (-5 / 100) * 100 = -5%
The calculated mark-up after adjusting for the profit margin is still negative. This means that the shopkeeper cannot achieve both the desired profit margin of 20% and the minimum discount of 25% simultaneously.
Therefore, the correct option is A) 60%, which suggests that the shopkeeper needs to mark up the price by at least 60% over the cost price to achieve the desired profit margin and offer the minimum discount.
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Community Answer
A shopkeeper wants to earn a profit of 20% and at the same time, the m...
Let CP = Rs 100
SP = Rs 120
MP = x
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