Question

If $p$ varies inversely as $q$ and directly as $r$ such that the constant of proportionality is 1. What will be the percentage change in $p$ due to an increase of 20% in $q$ and a decrease of 20% in $r$?

• A. 30%
• B. 33.33%
• C. 32.50%
• D. 34%

Answer 1

The correct option is B 33.33%

Given,
$p\propto \frac{1}{q}$
$p\propto r$
$\text{or,}p\propto \frac{r}{q}$
Since, the constant of proportionality is equal to 1,
$\text{So,}p=\frac{r}{q}$

$q$ increases by 20%
$\therefore q_{new}=q+\frac{20}{100}\times q=\frac{120q}{100}$

$r$ decreases by 20%
$\therefore r_{new}=r-\frac{20}{100}\times r=\frac{80r}{100}$
$\text{or,}{p}_{new}=\frac{\frac{80r}{100}}{\frac{120q}{100}}=\frac{80r}{120q}$

$\text{Change in}p=\frac{r}{q}-\frac{80r}{120q}=\frac{40r}{120q}$

$\text{\% change in}p$
$=\frac{\frac{40r}{120q}}{\frac{r}{q}}\times 100$
$=\frac{40r}{120q}\times \frac{q}{r}\times 100=33.33\text{\%}$