A jobber buys an article at $24 less 1212%. He then wishes to sell the article at a gain of 3313% of his cost after allowing a 20% discount on his marked price. At what price, in dollars, should the article be marked?

1964 AMC 12 Problem 9

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A jobber buys an article at

\$24

less

12\dfrac12\%.

He then wishes to sell the article at a gain of

33\dfrac13\%

of his cost after allowing a

20\%

discount on his marked price. At what price, in dollars, should the article be marked?

25.20

30.00

33.60

40.00

none of these

Compute the discounted cost first, then increase it by one third

The selling price is

80\%

of the marked price

The cost is

24(1-\frac{1}{8})=21

dollars. A gain of one third makes the desired selling price

21(\frac{4}{3})=28

dollars. If

M

is the marked price, then

0.8M=28,

M=35.

This is not listed.

Thus, the correct answer is E.