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