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, $1/16:1/36$

$=\sqrt{\left( {1}/{16}\; \right)}:\sqrt{\left( {1}/{36}\; \right)}$

$={\scriptstyle{}^{1}/{}_{4}}:{1}/{6}\;$

$={\left( {\scriptstyle{}^{1}/{}_{4}} \right)}/{\left( {1}/{6}\; \right)}\;$

$=\left( {\scriptstyle{}^{1}/{}_{4}} \right)\times \left( {6}/{1}\; \right)$

$={3}/{2}\;$

Therefore, sub – duplicate ratio is $3:2$

Solution:

Given, $9{{a}^{2}}/5:25{{a}^{2}}/3$

= √(9a²/5): √(25a²/3)

$=\sqrt{\left( 9{{a}^{2}}/5 \right)}:\sqrt{\left( 25{{a}^{2}}/3 \right)}$

$=3a\left( 1/\sqrt{5} \right):5a\left( 1/\sqrt{3} \right)$

$=3\sqrt{\sqrt{3}}:5\sqrt{5}$

Therefore, sub – duplicate ratio is $3\sqrt{3}:5\sqrt{5}$