Question

If a:b=2:5 then the value of (2a+3b):(7a+5b)​

Answer 1

According to question,

ab=25:2a+3b7a+5b=2ab+37ab+5

=2×25+37×25+5

=(19/5)(39/5)

=19/5×5/39

=19/39

Answer 2

Given

a:b = 2:5

$\implies \frac{a}{b} = \frac{2}{5}$

To Find

the value of (2a+3b):(7a+5b)

Calculations

$(2a+3b):(7a+5b) = \dfrac{2a + 3b}{7a + 5b} \\ \\ \\ dividing \: num \: and \: den \: by \: b \\ \\ \\ \implies \dfrac{ \dfrac{2a}{b} + 3 }{ \dfrac{7a}{b} + 5 } \\ \\ \\ putting \: \dfrac{a}{b} = \dfrac{2}{5} \\ \\ \\ \implies \: \dfrac{ \dfrac{2a}{b} + 3 }{ \dfrac{7a}{b} + 5} = \dfrac{2( \dfrac{2}{5}) + 3 }{7( \dfrac{2}{5}) + 5 } \\ \\ \\ = \dfrac{ \dfrac{4}{5} + 3}{ \dfrac{14}{5} + 5 } \\ \\ \\ = \dfrac{ \dfrac{19}{5} }{ \dfrac{39}{5} } \\ \\ \\ = \dfrac{19}{39}$

Result

(2a+3b):(7a+5b) = 19:39