Consider the following statements about clocks.
I. In one hour, the minute hand of a correct clock gains 330° on the hour hand.
II. A clock that loses 5 minutes every day is set right at 12 noon on a Sunday. At 12 noon (correct time) on the following Thursday, it shows 11:35 a.m.
Which of the above is/are correct?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Only I
The minute hand turns 6° a minute and the hour hand 0.5° a minute. A clock that loses time falls behind by its daily loss for each full day that passes.
I. In one hour, the minute hand of a correct clock gains 330° on the hour hand. Correct.
In 60 minutes the minute hand turns \(60\times6^\circ=360^\circ\)
In 60 minutes the hour hand turns \(60\times0.5^\circ=30^\circ\)
Gain \(=360^\circ-30^\circ=330^\circ\)
II. At 12 noon on the following Thursday, it shows 11:35 a.m. Incorrect.
From Sunday noon to Thursday noon is 4 days (Sunday to Monday, Monday to Tuesday, Tuesday to Wednesday, Wednesday to Thursday)
Loss \(=4\times5=20\) minutes
The clock shows 12:00 \(-\) 20 minutes \(=\) 11:40 a.m., not 11:35 a.m. (11:35 would need 5 days)