Symbiosis National Aptitude Test SNAP 2019 Paper

Given, x = $\frac{4\mathit{a}\mathit{b}}{\mathit{a}+\mathit{b}}$
⇒ $\frac{\mathit{x}}{2\mathit{a}}$ = $\frac{2\mathit{b}}{\mathit{a}+\mathit{b}}$
Applying componendo and dividendo, we get
$\frac{\mathit{x}+2\mathit{a}}{\mathit{x}-2\mathit{a}}$ = $\frac{2\mathit{b}+\mathit{a}+\mathit{b}}{2\mathit{b}-\mathit{a}-\mathit{b}}$ = $\frac{\mathit{a}+3\mathit{b}}{\mathit{b}-\mathit{a}}$ ... (i)
Also, $\frac{\mathit{x}}{2\mathit{b}}$ = $\frac{2\mathit{a}}{\mathit{a}+\mathit{b}}$
Applying componendo and dividendo, we get
$\frac{\mathit{x}+2\mathit{b}}{\mathit{x}-2\mathit{b}}$ = $\frac{2\mathit{a}+\mathit{a}+\mathit{b}}{2\mathit{a}-\mathit{a}-\mathit{b}}$ = $\frac{3\mathit{a}+\mathit{b}}{\mathit{a}-\mathit{b}}$ ... (ii)
From (i) & (ii),
$\frac{\mathit{x}+2\mathit{a}}{\mathit{x}-2\mathit{a}}+\frac{\mathit{x}+2\mathit{b}}{\mathit{x}-2\mathit{b}}$ = $\frac{\mathit{a}+2\mathit{b}}{\mathit{b}-\mathit{a}}+\frac{3\mathit{a}+\mathit{b}}{\mathit{a}-\mathit{b}}$
= $\frac{1}{\mathit{b}-\mathit{a}}$ [a + 3b - 3a - b]
= $\frac{2\left(\mathit{b}-\mathit{a}\right)}{\left(\mathit{b}-\mathit{a}\right)}$ = 2