Question

If a/b=2/3 and b/c=4/5 then the ratio a+b/b+c is equal to

Answer 1

Step-by-step explanation:

Given:

$\frac{a}{b} = \frac{2}{3} \\ \frac{a + b}{b} = \frac{2 + 3}{3}... (by \: componendo ) \\ \frac{a + b}{b} = \frac{5}{3} ..(1) \\ next \\ \frac{b}{c} = \frac{4}{5} \\ \\ \frac{c}{b} = \frac{5}{4}... (by \: invertendo) \\ \frac{c + b}{b} = \frac{5 + 4}{4}... ( by \: componendo) \\ \frac{b + c}{b} = \frac{9}{4}....(2) \\ dividing \: (1) \: by \: (2) \: we \: find : \\ \frac{ \frac{a + b}{b} }{ \frac{b + c}{b} } = \frac{ \frac{5}{3} }{ \frac{9}{4} } \\ \frac{a + b}{b} \times \frac{b}{b + c} = \frac{5}{3} \times \frac{4}{9} \\ \frac{a + b}{b + c} = \frac{20}{27}$