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:

$\dfrac1{1+p}$

$\dfrac1{1-p}$

$\dfrac p{1+p}$

$\dfrac p{p-1}$

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

Answer: C

Concepts:revenue percentage change algebraic equation

Difficulty rating: 1590

Small Hint:

Represent the new price and number sold by factors $1+p$ and $1-d$

Big Hint:

Equal revenue requires $(1+p)(1-d)=1$

Solution:

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.

1953 AMC 12 Problem 43

Answer: C

Difficulty rating: 1590

Small Hint:

Big Hint:

Solution:

Problem 43 in Other Years