Question

If $\frac{5a+2b}{5a-2b}=\frac{5}{3}$, then a : b =

• A. $\frac{8}{3}$
• B. $\frac{8}{5}$
• C. $\frac{5}{8}$
• D. $\frac{3}{8}$

Answer 1

The correct option is B

$\frac{8}{5}$

$\frac{5a+2b}{5a-2b}=\frac{5}{3}$

$\frac{5a+2b+5a-2b}{5a+2b-5a+2b}=\frac{5+3}{5-3}$ [Applying componendo and dividendo]

$\frac{10a}{4b}=\frac{8}{2}$

$\frac{2\left(5a\right)}{2\left(2b\right)}=\frac{8}{2}$

$\frac{a}{b}=\frac{8}{5}$