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

• A. $\frac{1}{1+p}$
• B. $\frac{1}{1-p}$
• C. $\frac{p}{1+p}$
• D. $\frac{p}{p-1}$
• E. $\frac{1-p}{1+p}$

Answer 1

Answer: (C)

$\frac{p}{1+p}$

Let $s$ be the price of the article, $n$ the number of sales. Then
$\left[\right(1+p\left)s\right]\left[\right(1-d\left)n\right]=sn$m
$p-d-pd=0,d=p/(1+p)$.