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,
$m:n=3:8$
$m/n=3/8$
$\left( 3m+2n \right)/\left( 5m/n \right)$
Now, divide both numerator and denominator by $’n’$we get,
$=\left[ \left( 3m/n \right)+\left( 2n/n \right) \right]/\left[ \left( 5m/n \right)+\left( n/n \right) \right]$
$=\left[ \left( 3m/n \right)+2 \right]/\left[ \left( 5m/n \right)+1 \right]$
Now, substitute the value of m and n we get,
$=\left[ \left( 3\left( 3/8 \right) \right)+2 \right]/\left[ \left( 5\left( 3/8 \right) \right)+1 \right]$
$=\left( \left( 9/8 \right)+2 \right)/\left( \left( 15/8 \right)+1 \right)$
$=25/23$
Therefore, the value of $\left( 3m+2n \right):\left( 5m+n \right)=25:23$