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,

$a:b=4:7$

$a/b=4/7$

$\left( 5a-4b \right)/\left( 2a-3b \right)$

Now, divide both numerator and denominator by $’b’$ we get,

$=\left[ \left( 5a/b \right)-\left( 4b/b \right) \right]/\left[ \left( 2a/b \right)-\left( 3b/b \right) \right]$

$=\left[ \left( 5a/b \right)-4 \right]/\left[ \left( 2a/b \right)-3 \right]$

Now, substitute the value of $a$ and $b$ we get,

$\left[ \left( 5\left( 4/7 \right) \right)-4 \right]/\left[ \left( 2\left( 4/7 \right) \right)-3 \right]$

$=\left( \left( 20/7 \right)-4 \right)/\left( \left( 8/7 \right)-3 \right)$

$=-8/-13$

$=8/13$