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A man sold an article at k percent profit after

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A man sold an article at k percent profit after

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A man sold an article at k percent profit after offering k percent discount on the listed price. Had he sold the article at (k+15) percent discount on the listed price, his profit would have been (k-20) percent. What would have been his percent profit had he sold the article without offering any discount?

A) 5%
B) 10%
C) 25%
D) 33%
E) 38%

The OA is the option D.

Experts, I am a little confused here. May you help me, please? I would be thankful.

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VJesus12 wrote:
A man sold an article at k percent profit after offering k percent discount on the listed price. Had he sold the article at (k+15) percent discount on the listed price, his profit would have been (k-20) percent. What would have been his percent profit had he sold the article without offering any discount?

A) 5%
B) 10%
C) 25%
D) 33%
E) 38%
Let:
L = the list price.
C = the cost price.
x = the difference between the two reduced prices.

Discount = percentage of the LIST price.
Since x increases the discount by 15% -- from k to k+15 -- x must be equal to 15% of the LIST price:
x = (15/100)L.

Profit = percentage of the COST price.
Since x decreases the profit by 20% -- from k to k-20 -- x must be equal to 20% of the COST price:
x = (20/100)C.

Since the expressions in blue both represent the value of x, they must be equal:
(15/100)L = (20/100)C
15L = 20C
3L = 4C
L = (4/3)C.

The resulting equation indicates that the list price is 1/3 greater than the cost price, implying that the regular profit is 1/3 of the cost price:
Profit = (1/3)C = 33.33%.

The correct answer is D.

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