A number whose fifth part increased by 4 is equal to its fourth part diminished by 10, is :

Answer: Option D

Let the number be x
Then,
$$\begin{array}{rl}& \iff \left(\frac{1}{5}x+4\right)=\left(\frac{1}{4}x-10\right)\\ & \iff \frac{x}{20}=14\\ & \iff x=14\times 20\\ & \iff x=280\end{array}$$