1969 AMC 12 Problem 2

Attempt Problem 2 of the 1969 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 1969 AMC 12 solutions, or check the answer key.

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

If an item is sold for

x

dollars, there is a loss of

15\%

based on the cost. If, however, the same item is sold for

y

dollars, there is a profit of

15\%

based on the cost. The ratio

y:x

is:

23:17

17y:23

23x:17

dependent upon the cost

none of these

Let the cost be

C

Write

x=0.85C

and

y=1.15C,

then form the ratio

If the cost is

C,

then

x=0.85C

and

y=1.15C.

Therefore

\begin{aligned} y:x&=1.15C:0.85C\\ &=115:85=23:17. \end{aligned}

Therefore, the correct answer is A.

Problem 2 in other years