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If the maximum discount that a merchant who doesn’t want to sell an item at a loss can offer on that item is 20%, what will be the
profit percentage that the merchant makes if he sells the item at its marked price?
  • a)
    12.5%
  • b)
    20%
  • c)
    25%
  • d)
    33%
  • e)
    Cannot be determined
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If the maximum discount that a merchant who doesn’t want to sell...
Given:
  • Let Cost Price of the item be C, Marked Price be M and Selling Price be S
    • Maximum discount for no loss = 20%
      • This means, At 20% discount, the item is sold at Zero Profit, Zero Loss
      • That is, At 20% discount, the discounted price of the item is equal to the Cost Price
To Find: % Profit if the item is sold at its Marked Price
Approach:
    • So, to answer this question, we need to find the ratio M/C
  1. We are given one relation between M and C : At 20% discount on M, the discounted price is equal to the cost price. Using this relation, we’ll find the required ratio.
Working out:
  • (Value of 20% Discount) = 20% of M = 0.2M
    • This is the maximum discount that the merchant can offer without going into loss
    • This means, at this point, his profit is zero (if the selling price was any lesser, he would make a loss)
    • So, at this discount, his selling price is equal to his cost price
  • Now, (Selling price at 20% discount on M) = M – (Value of 20% Discount) = M – 0.2M = 0.8M
  • So, 0.8M = C
  • So, Required % Profit 
Looking at the answer choices, we see that the correct answer is Option C
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Most Upvoted Answer
If the maximum discount that a merchant who doesn’t want to sell...
Understanding the Scenario
To determine the profit percentage when a merchant sells an item at its marked price, we start by defining key variables:
- **Cost Price (CP)**: The price the merchant pays for the item.
- **Marked Price (MP)**: The original selling price before any discounts.
- **Maximum Discount**: The highest discount the merchant is willing to offer, which is 20%.

Calculating the Selling Price
When a maximum discount of 20% is applied to the marked price, the selling price (SP) can be expressed as:
- SP = MP - (20% of MP)
- SP = MP × (1 - 0.20)
- SP = MP × 0.80

Ensuring No Loss
Since the merchant does not want to sell the item at a loss, the selling price (SP) must be equal to or greater than the cost price (CP). Thus, we can say:
- SP = CP
- MP × 0.80 = CP
From this, we can express CP in terms of MP:
- CP = MP × 0.80

Calculating Profit Percentage
Profit is calculated as:
- Profit = MP - CP
- Profit = MP - (MP × 0.80)
- Profit = MP × (1 - 0.80)
- Profit = MP × 0.20
Now, the profit percentage can be calculated using the formula:
- Profit Percentage = (Profit / CP) × 100
- Profit Percentage = [(MP × 0.20) / (MP × 0.80)] × 100
- Profit Percentage = (0.20 / 0.80) × 100
- Profit Percentage = 0.25 × 100
- Profit Percentage = 25%

Conclusion
Hence, the profit percentage when the merchant sells the item at its marked price is **25%**, making the correct answer option **C**.
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