At what time between 5:30 and 6 o’clock, will the hands of a clock be at right angle?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(43\displaystyle\frac{7}{11}\) min past 5
The minute hand turns 6° a minute and the hour hand 0.5° a minute. At 5 o’clock the hour hand is at \(5\times30^\circ=150^\circ\) from 12, so m minutes later the angle between the hands is \(150^\circ+0.5m-6m\).
Between 5:30 and 6 the minute hand has passed the hour hand, so the angle is \(5.5m-150=90\)
\(5.5m=240\)
\(\displaystyle m=\frac{240}{5.5}=\frac{480}{11}=43\frac{7}{11}\) minutes
The other right angle of this hour comes at \(\displaystyle 10\frac{10}{11}\) min past 5, before 5:30, so it does not count.