Diameter of a jar cylindrical in shape is increased by 25%. By what percent must the height be decreased so that there is no change in its volume :

Answer: Option C

Let original radius = r and original height = h
Original volume = $$\pi r^{2}h$$
New radius = 125% of r = $$\frac{5r}{4}$$
Let new height = H
Then,
$$\begin{array}{rl}& \pi r^{2}h=\pi {\left(\frac{5r}{4}\right)}^2\times H\\ & Or,H=\frac{16}{25}h\end{array}$$
Decrease in height :
$$\begin{array}{rl}& =\left(h-\frac{16h}{25}\right)\\ & =\frac{9h}{25}\end{array}$$
∴ Decrease % :
$$\begin{array}{rl}& =\left(\frac{9h}{25}\times \frac{1}{h}\times 100\right)\%\\ & =36\%\end{array}$$