1972 AMC 12 Problem 2

Attempt Problem 2 of the 1972 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1972 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

If a dealer could get his goods for

8\%

less while keeping his selling price fixed, his profit, based on cost, would be increased to

(x+10)\%

from his present profit of

x\%,

which is:

12\%

15\%

30\%

50\%

75\%

Let the present cost be

C

and express the same selling price in two ways

The reduced cost is

0.92C

and its profit rate is

(x+10)\%

The fixed selling price gives

\begin{aligned} 1+0.01x&=0.92\\ &\quad+0.0092(x+10). \end{aligned}

Simplifying yields

1+0.01x=1.012+0.0092x,

0.0008x=0.012

and

x=15.

Therefore, the correct answer is B.

Problem 2 in other years