In a certain time, the hour hand of a correct clock turns through 17°. Through how many degrees does the minute hand turn in the same time?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 204°
The hour hand turns 0.5° a minute and the minute hand 6° a minute, so in any time the minute hand turns 12 times as far as the hour hand.
Time for the hour hand to turn 17° \(=\displaystyle\frac{17}{0.5}=34\) minutes
Turn of the minute hand in 34 minutes \(=34\times6^\circ=204^\circ\)
Check: \(17^\circ\times12=204^\circ\)
Why the other options are incorrect
Option (1) 102° — Incorrect. This multiplies by 6; the minute hand is 12 times as fast, not 6.
Option (2) 187° — Incorrect. This multiplies by 11, the rate at which the minute hand gains on the hour hand, not its own turn.
Option (3) 221° — Incorrect. This multiplies by 13, which has no meaning on a clock.