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:

From the question it is given that, $p:q=2:5,q:r=4:3$

So, $p/q=2/5$

$q/r=4/3$

$\left( p/q \right)\times \left( q/r \right)=\left( 2/5 \right)\times \left( 4/3 \right)$

By simplification we get,

$p/r=8/15$

Therefore, the value of $p:r=8:15$