If the radius of a circle is increased by 75%, then its circumference will increase by :

Answer: Option C

Let original radius be R cm
Then, original circumference = $$2\pi r$$ cm
New radius :
$$\begin{array}{rl}& =\left(175\%\text{ of }R\right)cm\\ & =\left(\frac{175}{100}\times R\right)cm\\ & =\frac{7R}{4}cm\end{array}$$
New circumference :
$$\begin{array}{rl}& =\left(2\pi \times \frac{7R}{4}\right)cm\\ & =\frac{7\pi R}{2}cm\end{array}$$
Increase in circumference :
$$\begin{array}{rl}& =\left(\frac{7\pi R}{2}-2\pi R\right)cm\\ & =\frac{3\pi R}{2}cm\end{array}$$
Increase % :
$$\begin{array}{rl}& =\left(\frac{3\pi R}{2}\times \frac{1}{2\pi R}\times 100\right)\%\\ & =75\%\end{array}$$