Clocks Questions and Answers

Answer: A

Correct answer: 38 (2/11) min past 1

At 1 o’clock the hour hand is \(30°\) ahead. To be opposite, the minute hand must pass it and then lead by \(180°\), a total relative gain of \(30 + 180 = 210°\).

\[t = \frac{210}{5.5} = \frac{420}{11} = 38\tfrac{2}{11}\ \text{minutes}\]

So the hands are opposite at \(38\tfrac{2}{11}\) minutes past 1.

Answer: B

Correct answer: 22 cm

In 30 minutes the minute hand sweeps half a revolution, so its tip traces a semicircle of radius 7 cm.

\[\text{Distance} = \pi r = \frac{22}{7} \times 7 = 22 \text{ cm}\]

A full hour would carry the tip the whole circumference, \(2\pi r = 44\) cm.

Answer: C

Correct answer: 120°

The minute hand completes \(360°\) in 60 minutes, so it turns \(6°\) each minute.

\[20 \times 6 = 120°\]

This is a third of the dial, matching the fact that 20 minutes is a third of an hour.

Answer: D

Correct answer: 5 (5/11) min past 4

At 4 o’clock the hour hand leads by \(120°\). For the first right angle the minute hand must reduce that lead to \(90°\), a relative gain of \(30°\).

\[t = \frac{30}{5.5} = \frac{60}{11} = 5\tfrac{5}{11}\ \text{minutes}\]

The second right angle in that hour comes when the minute hand has gained \(210°\), at \(38\tfrac{2}{11}\) minutes past 4.

Answer: D

Correct answer: 9:10 a.m.

From one Monday to the next is exactly 7 days.

\[\text{Total gain} = 7 \times 10 = 70 \text{ minutes} = 1 \text{ hour } 10 \text{ minutes}\]

Running ahead by that amount, the clock shows 9:10 a.m. when the true time is 8 a.m.

Answer: B

Correct answer: 130°

The minute hand moves \(6°\) per minute and the hour hand \(0.5°\) per minute.

\[\text{Minute hand} = 40 \times 6 = 240°\]

\[\text{Hour hand} = 3 \times 30 + 40 \times 0.5 = 90 + 20 = 110°\]

\[\text{Angle} = 240 - 110 = 130°\]

The hour hand has crept two-thirds of the way from 3 towards 4, which is what the extra \(20°\) represents.

Answer: A

Correct answer: 22

The hands point in opposite directions once for every full \(360°\) the minute hand gains on the hour hand. That gain happens 11 times in 12 hours, so the hands are opposite 11 times in 12 hours and 22 times in 24 hours.

The same reasoning gives 22 coincidences in 24 hours, since each relative revolution produces exactly one of each.

Answer: C

At 3 o’ clock, the hour hand is at 90 degrees from the vertical. In 40 minutes,
Hour hand = 90 + 40*(0.5) = 90 + 20 = 110 (The hour hand moves at 0.5 dpm)
Minute hand = 40*(6) = 240 (The minute hand moves at 6 dpm)
Difference or angle between the hands = 240 - 110 = 130 degrees.

Answer: A

At 9 o’ clock, the hour hand is at 270 degrees from the vertical. In 20 minutes,
Hour hand = 270 + 20*(0.5) = 270 + 10 = 280 (The hour hand moves at 0.5 dpm)
Minute hand = 20*(6) = 120 (The minute hand moves at 6 dpm)
Difference or angle between the hands = 280 - 120 = 160 degrees.

Answer: A

In a clock, 12 hours form 360° degree. So one hour forms 30°. Therefore 7 hours form 210° (30° X 7) degree. In a minute, hour hand moves 0.5° degree, so in 10 minutes it moves 0.5° X 10 = 5°
Thus, by 10 Minutes past 7, hour hand has turn through 210° + 5° = 215°