Management Aptitude Test 2014 Paper

(a) Let the radius of smaller circle be r cm
and radius of larger circle = R cm.

Difference between the area = 116π
$\mathit{\pi }{\mathit{R}}^2+\mathit{\pi }{\mathit{r}}^2$ = 116π
${\mathit{R}}^2+{\mathit{r}}^2$ =116 ........(i)
Also, the difference between their centres = 6 cm
i.e., R - r = 6
or R= (6 + r) .........(ii)
From Eqs. (i) and (ii),
${\left(6+\mathit{r}\right)}^2+{\mathit{r}}^2$ = 116
⇒ 36+ ${\mathit{r}}^2$ + 12r + ${\mathit{r}}^2$ = 116
⇒ 2${\mathit{r}}^2$ + 12r + 36 - 116 = 0
⇒ 2${\mathit{r}}^2$ + 12r - 80 = 0
⇒ ${\mathit{r}}^2$ + 6r - 40 = 0
⇒ ${\mathit{r}}^2$ + 10r - 4r - 40 = 0
⇒ (r + 10) (r - 4) = 0
∴ r = -10, 4 (radiuscannot be negative)
∴ Radius of smaller circle = 4 cm
Radius of larger circle = 4 + 6 = 10 cm