The ratio is used for comparing two quantities of the sane kind.
The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in proportion.
The concept of ratio and proportion is majorly based on ratios and fractions.
Solution:
Given ratio,${{a}^{3}}{{b}^{2}}:{{a}^{2}}{{b}^{2}}$
The reciprocal of the given ratio is
$1/{{a}^{3}}{{b}^{2}}:1/{{a}^{2}}{{b}^{3}}$
$=\left( 1/{{a}^{3}}{{b}^{2}} \right)\times \left( {{a}^{2}}{{b}^{3}}/1 \right)$
$=b:a$
Therefore, reciprocal of the ratio is $b:a$
Solution:
Given ratio,
$81p{{q}^{2}}:54{{p}^{2}}q$
The reciprocal of the given ratio
$\left( 1/81p{{q}^{2}} \right):1/54{{p}^{2}}q$
$=\left( 1/81p{{q}^{2}} \right)\times \left( {{54}^{2}}q/1 \right)$
By simplification we get,
$=2p/3q$
Therefore, reciprocal of the ratio is $2p:3q$