SSC CGL 1 Sep 2016 Paper

$\frac{{\mathit{a}}^2}{\mathit{b}+\mathit{c}}$ = $\frac{{\mathit{b}}^2}{\mathit{c}+\mathit{a}}$ = $\frac{{\mathit{c}}^2}{\mathit{a}+\mathit{b}}$ = 1
⇒ $\frac{{\mathit{a}}^2}{\mathit{b}+\mathit{c}}$ = 1
⇒ ${\mathit{a}}^2$ = b + c
⇒ ${\mathit{a}}^2$ + a = a + b + c
⇒ a (a + 1) = a + b + c
⇒ $\frac{1}{\mathit{a}+1}$ = $\frac{\mathit{a}}{\mathit{a}+\mathit{b}+\mathit{c}}$
Similarly,
$\frac{{\mathit{b}}^2}{\mathit{c}+\mathit{a}}$ = 1 ⇒ ${\mathit{b}}^2$ = c + a
⇒ ${\mathit{b}}^2$ + b = a + b + c
⇒ b (b + 1) = a + b + c
⇒ $\frac{1}{\mathit{b}+1}$ = $\frac{\mathit{b}}{\mathit{a}+\mathit{b}+\mathit{c}}$
and $\frac{{\mathit{c}}^2}{\mathit{a}+\mathit{b}}$ = 1 ⇒ ${\mathit{c}}^2$ = a + b
⇒ ${\mathit{c}}^2$ + c = a + b + c
⇒ c (c + 1) = a + b + c
⇒ $\frac{1}{1+\mathit{a}}$ + $\frac{1}{1+\mathit{b}}$ + $\frac{1}{1+\mathit{c}}$ = $\frac{\mathit{a}}{\mathit{a}+\mathit{b}+\mathit{c}}$ + $\frac{\mathit{b}}{\mathit{a}+\mathit{b}+\mathit{c}}$ + $\frac{\mathit{c}}{\mathit{a}+\mathit{b}+\mathit{c}}$
= $\frac{\mathit{a}+\mathit{b}+\mathit{c}}{\mathit{a}+\mathit{b}+\mathit{c}}$ = 1