By what percent the volume of a cube increases if the length of each edge was increased by 50%

Answer: Option C

Let original edge = a
Then, original volume = a³
New edge :
$$\begin{array}{rl}& =\frac{150}{100}a\\ & =\frac{3a}{2}\end{array}$$
New volume :
$$\begin{array}{rl}& ={\left(\frac{3a}{2}\right)}^3\\ & =\frac{27a^3}{8}\end{array}$$
Increase in volume :
$$\begin{array}{rl}& =\left(\frac{27a^3}{8}-a^3\right)\\ & =\frac{19a^3}{8}\end{array}$$
∴ Increase % :
$$\begin{array}{rl}& =\left(\frac{19a^3}{8}\times \frac{1}{a^3}\times 100\right)\%\\ & =237.5\%\end{array}$$