Question

a:b=6:5(a+b):(3a-2b)

Answer 1

Given that the ratio a and b is 6 : 5

$\bold{a : b = 6 : 5} \: \: \: \: \: \: \: \: \: - - - - - - - : ( \: 1 \: )$




Then,


= > ( a + b ) : ( 3a - 2b )

$= \: > \: \: \frac{ \frac{a + b}{b} }{ \frac{3a - 2b}{b} } \\ \\ \\ = > \frac{ \frac{a}{b} + \frac{b}{b} }{ \frac{3a}{b} - \frac{2b}{b} } \\ \\ \\ \\ From \: ( i ), \: putting \: the \: value \: of \: a : b \: t hat \: is \: \: 6 : 5 \\ \\ \\ \\ = > \frac{ \frac{6}{5} + \frac{ \cancel{b}}{ \cancel{b}} }{3( \frac{6}{5} ) - 2( \frac{ \cancel{b}}{ \cancel{b}}) } \\ \\ \\ \\ = > \frac{ \frac{6}{5} + 1}{ \frac{3 \times 6}{5} - 2} \\ \\ \\ \\ = > \frac{ \frac{6 + 5}{5} }{ \frac{18 - 10}{5}} \\ \\ \\ \\ = > \frac{ \frac{11}{ \cancel{5}} }{ \frac{8}{ \cancel{5}} } \\ \\ \\ \\ = > \frac{11}{8}$