UKMT Junior Kangaroo, 2018

My TV screen has sides in the ratio $16:9$. My mother's TV screen has sides in the ratio $4:3$. A picture which exactly fills the screen of my TV only fills the width of the screen of my mother's TV. What fraction of the screen on my mother's TV is not covered?

(A) $\frac{1}{6}$ (B) $\frac{1}{5}$ (C) $\frac{1}{4}$ (D) $\frac{1}{3}$ (E) It depends on the size of the screen.