1952 AMC 12 Problem 17

Question

A merchant bought some goods at a discount of

20\%

of the list price. He wants to mark them at such a price that he can give a discount of

20\%

of the marked price and still make a profit of

20\%

of the selling price. The percent of the list price at which he should mark them is:

20

100

125

80

120

Normalize the list price to

1

and distinguish cost, marked price, and selling price

A profit equal to

20\%

of selling price means the cost is

80\%

of selling price

Let the list price be

1.

The merchant’s cost is

0.8.

If the selling price is

S,

then

S-0.8=0.2S,

so

S=1.

If the marked price is

M,

the

20\%

discount gives

0.8M=S=1,

hence

M=1.25.

The marked price must therefore be

125\%

of the list price, so the correct answer is C.

Problem 17 in other years