Consider the following statements about a correct clock.
I. When the clock shows 5:20, its image in a plane mirror placed vertically beside it shows 6:40.
II. The hour hand turns through 80° from 9:30 a.m. to 12 noon.
III. The hour hand makes exactly 5 complete rounds in 2½ days.
Which of the above statements are correct?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → I and III only
In a vertical mirror the image time is 11:60 minus the clock time. The hour hand turns 0.5° a minute and goes once round in 12 hours.
I. When the clock shows 5:20, its mirror image shows 6:40. Correct.
Image time \(=\) 11:60 \(-\) 5:20 \(=\) 6:40
II. The hour hand turns through 80° from 9:30 a.m. to 12 noon. Incorrect.
9:30 a.m. to 12 noon \(=2\) hours 30 minutes \(=150\) minutes
Turn \(=150\times0.5^\circ=75^\circ\), not 80°
III. The hour hand makes exactly 5 complete rounds in 2½ days. Correct.
2½ days \(=2.5\times24=60\) hours
Rounds \(=\displaystyle\frac{60}{12}=5\)