Question

If $\frac{a}{b}=\frac{7}{3}$ then find the value of the ratio $\frac{a+2b}{a-2b}$

Answer 1

▪︎■ ANSWER ■▪︎

We can find the ratio for the following question by 2 methods -

$\rightarrow\bf\underline{METHOD-1}$

Let a = 7m , b = 3m

$\therefore\frac{a+2b}{a-2b}=\frac{7m+2×3m}{7m-2×3m}$

$=\frac{7m+6m}{7m-6m}$

$\frac{13m}{m}=\frac{13}{1}$

$\rightarrow\bf\underline{METHOD-2}$

$\therefore\frac{a}{b}=\frac{7}{3}$

$\therefore\frac{a}{2b}=\frac{7}{6}$...(multiplying both sides by $\frac{1}{2}$

$\therefore\frac{a+2b}{a-2b}=\frac{7+6}{7-6}$(using componendo - dividendo)

$\therefore\frac{a+2b}{a-2b}=\frac{13}{1}$

Answer 2

Answer :

a/b=7/3

a/b=28/12=7/3

12a=28b

a+2b=13a-26b

a+2b=13(a-2b)

a+2b/a-2b=13

So, ratio is 13 : 1

$\rule{100}{2}$