1950 AMC 12 Problem 36

Question

A merchant buys goods at

25\%

off the list price. He desires to mark the goods so that he can give a discount of

20\%

on the marked price and still clear a profit of

25\%

on the selling price. What per cent of the list price must he mark the goods?

125\%

100\%

120\%

80\%

75\%

Take the list price to be

L

and the marked price to be

M

The cost is

0.75L,

the selling price is

0.8M,

and the cost is

75\%

of the selling price

Let the list and marked prices be

L

and

M.

The merchant’s cost is

0.75L,

while the selling price after the discount is

0.8M.

A profit equal to

25\%

of the selling price means that the cost is the remaining

75\%

of that price. Therefore

0.75L=0.75(0.8M)=0.6M.

Thus

M=1.25L,

or

125\%

of the list price.

Thus, the correct answer is A.

Problem 36 in other years