NIMCET 2014 Question Paper with solutions

We have,
${\mathit{x}}^2+\mathit{y}\sqrt{\mathit{x}\mathit{y}}$ = 336
⇒ $\sqrt{\mathit{x}}\left(\mathit{x}\sqrt{\mathit{x}}+\mathit{y}\sqrt{\mathit{y}}\right)$ = 366 ... (i)
and ${\mathit{y}}^2$ + x$\sqrt{\mathit{x}\mathit{y}}$ = 11
⇒ $\sqrt{\mathit{y}}\left(\mathit{y}\sqrt{\mathit{y}}+\mathit{x}\sqrt{\mathit{x}}\right)$ = 112 ... (ii)
Dividing Eq. (i) by Eq. (ii), we get
$\frac{\sqrt{\mathit{x}}}{\sqrt{\mathit{y}}}$ = 3 or x = 9y
From Eq. (i), $81{\mathit{y}}^2$ + y $\sqrt{9{\mathit{y}}^2}$ = 336
or $81{\mathit{y}}^2$ + $3{\mathit{y}}^2$ = 336
⇒ ${\mathit{y}}^2$ = 4 , y = 2
⇒ x = 18
∴ x + y = 18 + 2 = 20