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. <i class="em em-disappointed"></i>
A man sold an article at k percent profit after
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Let: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%
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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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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