A merchant sells an item at a 20% discount, but still makes a gross profit of 20 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount?

সঠিক উত্তর

50%

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Question: A merchant sells an item at a 20% discount, but still makes a gross profit of 20 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount?

Solution:
Let the Market Price of the product be MP.
Let the Original Cost Price of the product be CP.

Selling Price (Discounted Price) = 100%of MP - 20%MP = 80% of MP ....... (1)
Profit made by selling at discounted price = 20% of CP ....... (2)

Now, Profit = Selling Price - Original Cost Price
⇒ 20% of CP = 80% of MP - 100% CP
⇒ MP = 120CP/80 = 3/2 (CP)

Now if Product is sold without any discount, then,
Profit = Selling Price (without discount) - Original Cost Price
= Market Price - Original Cost Price
= MP - CP
= (3/2)CP - CP
= 1/2 CP
= 50% of CP

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60%

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