1953 AMC 12 Problem 43

Question

If the price of an article is increased by per cent

p,

then the decrease in per cent of sales must not exceed

d

in order to yield the same income. The value of

d

is:

\dfrac1{1+p}

\dfrac1{1-p}

\dfrac p{1+p}

\dfrac p{p-1}

\dfrac{1-p}{1+p}

Represent the new price and number sold by factors

1+p

and

1-d

Equal revenue requires

(1+p)(1-d)=1

Writing the percentage rates as fractions of the original quantities, equal income requires

(1+p)(1-d)=1.

Hence

p-d-pd=0,

so

d=\frac p{1+p}.

Thus, the correct answer is C.

Problem 43 in other years