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,
$a:b=4:7$
$a/b=4/7$
$\left( 5a+2b \right)/\left( 5a-2b \right)$
Now, divide both numerator and denominator by $’b’$ we get,
$=\left[ \left( 5a/b \right)+\left( 2b/b \right) \right]/\left[ \left( 5a/b \right)-\left( 2b/b \right) \right]$
$=\left[ \left( 5a/b \right)+2 \right]/\left[ \left( 5a/b \right)-2 \right]$
Now, substitute the value of a and b we get,
$=\left[ \left( 5\left( 4/7 \right) \right)+2 \right]/\left[ \left( 5\left( 4/7 \right) \right)-2 \right]$
$=\left( \left( 20/7 \right)+2 \right)/\left( \left( 20/7 \right)-2 \right)$
$=34/6$
$=17/3$
Solution:
From the question it is given that,
$a:b=4:7$
$a/b=4/7$
$\left( 6a-b \right)/\left( a+3b \right)$
Now, divide both numerator and denominator by $’b’$ we get,
$=\left[ \left( {6a}/{b}\; \right)-\left( {b}/{b}\; \right) \right]/\left[ \left( {a}/{b}\; \right)+\left( {3b}/{b}\; \right) \right]$ $=\left[ \left( {6a}/{b}\; \right)-1 \right]/\left[ \left( {a}/{b}\; \right)+3 \right]$
Now, substitute the value of a and b we get,
$=\left[ \left( 6\left( 4/7 \right) \right)-1 \right]/\left[ \left( a/b \right)+\left( 3b/b \right) \right]$
$=\left( \left( 24/7 \right)-1 \right)/\left( \left( 4/7 \right)+3 \right)$
$=17/25$