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What is the maximum percentage discount that a merchant can offer on her marked price so that she ends up selling at no profit or loss, if she had initially marked her goods up by 50%?
- a)50%
- b)20%
- c)25%
- d)16.67%
- e)33.33%
Correct answer is option 'E'. Can you explain this answer?
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Most Upvoted Answer
What is the maximum percentage discount that a merchant can offer on h...
Understanding the Marked Price and Cost Price
To determine the maximum percentage discount a merchant can offer while still achieving no profit or loss, we must first establish the relationship between the marked price (MP) and the cost price (CP).
- Marked Price (MP): The price after a 50% increase.
- Cost Price (CP): The original price before any markup.
If we assume the cost price (CP) is $100:
- Marked Price Calculation:
- MP = CP + 50% of CP
- MP = 100 + 50 = $150
Calculating the Selling Price for No Profit or Loss
To sell at no profit or loss, the selling price (SP) must equal the cost price (CP).
- Selling Price for No Profit or Loss:
- SP = CP = $100
Determining the Maximum Discount
Now, we need to find the maximum discount off the marked price (MP) that results in a selling price equal to the cost price.
- Discount Calculation:
- Let the discount be D.
- Selling Price (SP) = Marked Price (MP) - Discount (D)
- $100 = $150 - D
- D = $150 - $100 = $50
Calculating the Percentage Discount
To find the percentage discount based on the marked price:
- Percentage Discount:
- Percentage Discount = (Discount / Marked Price) × 100
- Percentage Discount = (50 / 150) × 100 = 33.33%
Conclusion
The maximum percentage discount that allows the merchant to sell at no profit or loss, despite a 50% markup, is 33.33%. Thus, the correct answer is option 'E'.
To determine the maximum percentage discount a merchant can offer while still achieving no profit or loss, we must first establish the relationship between the marked price (MP) and the cost price (CP).
- Marked Price (MP): The price after a 50% increase.
- Cost Price (CP): The original price before any markup.
If we assume the cost price (CP) is $100:
- Marked Price Calculation:
- MP = CP + 50% of CP
- MP = 100 + 50 = $150
Calculating the Selling Price for No Profit or Loss
To sell at no profit or loss, the selling price (SP) must equal the cost price (CP).
- Selling Price for No Profit or Loss:
- SP = CP = $100
Determining the Maximum Discount
Now, we need to find the maximum discount off the marked price (MP) that results in a selling price equal to the cost price.
- Discount Calculation:
- Let the discount be D.
- Selling Price (SP) = Marked Price (MP) - Discount (D)
- $100 = $150 - D
- D = $150 - $100 = $50
Calculating the Percentage Discount
To find the percentage discount based on the marked price:
- Percentage Discount:
- Percentage Discount = (Discount / Marked Price) × 100
- Percentage Discount = (50 / 150) × 100 = 33.33%
Conclusion
The maximum percentage discount that allows the merchant to sell at no profit or loss, despite a 50% markup, is 33.33%. Thus, the correct answer is option 'E'.
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Community Answer
What is the maximum percentage discount that a merchant can offer on h...
Step 1: Assume cost price and compute marked price
Approach: Assume cost price to be $100.
She had initially marked her goods up by 50%.
Therefore, a 50% mark up would have resulted in her marked price being $100 + 50% of $100 = $100 + $50 = $150.
Therefore, a 50% mark up would have resulted in her marked price being $100 + 50% of $100 = $100 + $50 = $150.
Step 2: Compute the % discount offered
She finally sells the product at no profit or loss.
i.e., she sells the product at cost price, which in this case is $100.
Therefore, she offers a discount of $50 on her marked price of $150.
i.e., she sells the product at cost price, which in this case is $100.
Therefore, she offers a discount of $50 on her marked price of $150.
Hence, the % discount offered by her = 
Discount offered is 33.33%
Discount offered is 33.33%
Choice E is the correct answer.
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What is the maximum percentage discount that a merchant can offer on her marked price so that she ends up selling at no profit or loss, if she had initially marked her goods up by 50%?a)50%b)20%c)25%d)16.67%e)33.33%Correct answer is option 'E'. Can you explain this answer?
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