A circular path is made from two concentric circular rings in such a way that the smaller ring when ...........

Quantitative Aptitude (CDS) Mensuration 2D

A circular path is made from two concentric circular rings in such a way that the smaller ring when allowed to roll over the circumference of the bigger ring, it takes three full revolutions. If the area of the pathway is equal to n times the area of the smaller ring, then n is equal to

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Explanation:

Since, the smaller ring takes three full revolutions to roll over the circumference of bigger ring.
$\therefore 2 \pi r = 3(2 \pi r_{1})$
$Area\: of \: pathway = \pi r^{2} - \pi r_{1}^{2}=n(\pi r_{1}^{2})$
$=>\pi r^{2} = (n+1))\pi r_{1}^{2}$
$=>r^{2}=(n+1)\frac{r^{2}}{9}$
$=>n=9-1=8$