When the minute hand travels $360^\circ$ the hour hand travels $360/12 = 30^\circ.$
So, in every hour the degree between the minute hand and hour hand changes by $30^\circ.$
In a minute the minute hand travels $360/60 = 6^\circ$ whereas the hour hand travels $(360/12)/60 = 0.5^\circ$
So, the degree between the hour and minute hands of the clock changes by $5.5^\circ$ every minute.
Thus we get a simple formula to find the angle between the hour and minute hands as $$5.5 M = 30H\pm \,\theta,$$ where
- $\text{M = minutes},$
- $\text {H = hours and }$
- $\,\theta = \text{angle between the hour and minute hands.}$
Now, $5.5 \times 40 = 30 \times 5 \pm \, \theta$
$\implies 220 = 150 \pm \theta$
$\implies \theta = 70^{\circ}.$
So, the correct answer is $(D).$