Banking Quantitative Aptitude Sample Paper Quantitative Aptitude Sample Paper-35

On increasing the diameter of a circle by 75%, the percentage increase in the perimeter is [SSC (CGL) 2014]

A) 76%

B) 80%

C) 65%

D) 70%

Correct Answer: A

Solution :

Let diameter of circle \[=d\]

Perimeters \[=2\pi r=\pi d\] \[[\because d=2r]\]

Then, new diameter \[=d+\frac{d\times 75}{100}=d+\frac{3d}{4}=\frac{7d}{4}\]

Now, new perimeter \[=\pi \times \frac{7d}{4}=\frac{7\pi d}{4}\]

\[\therefore \]Increase in perimeter \[=\frac{7\pi d}{4}-\pi d=\pi \left[ \frac{7d}{4}-d \right]\]

\[=\pi \left( \frac{3d}{4} \right)=\frac{3\pi d}{4}=\pi d\times \frac{3}{4}\]

Now, percentage increase in perimeter

\[=\frac{\pi d\times \frac{3}{4}}{\pi d}\times 100=\frac{3}{4}\times 100=75\]%