NIELIT 2022 Feb Scientist C - Section D: 2

Question

If $\frac{a}{a+b} = \frac{7}{17},$ then $\frac{2a-b}{a+b}$ is equal to :

• A. $\frac{4}{17}$
• B. $\frac{-3}{17}$
• C. $\frac{10}{17}$
• D. $\frac{8}{17}$

Answer 1

Given that:$\frac{a}{a+b}=\frac{7}{17}$

$\implies 17a=7a+7b$

$\implies 10a=7b$

$\implies a=\frac{7b}{10}…...(i)$

so the value of $\frac{2a-b}{a+b}=\frac{2\times \frac{7b}{10}-b}{\frac{7b}{10}+b}$

$\implies\frac{2b}{5}\times\frac{10}{17b}=\frac{4}{17}$

Option (A) is correct.