Clocks Questions and Answers

Answer: D

The hour hand sweeps the full \( 360^{\circ} \) in twelve hours, so it turns \( 30^{\circ} \) an hour.

\[ 8 \text{ hours} \times 30^{\circ} = 240^{\circ} \]

Only the hour hand is asked about; the minute hand would have turned \( 8 \times 360^{\circ} \) over the same period.

Answer: B

The hour hand turns \( 30^{\circ} \) an hour, or \( 0.5^{\circ} \) a minute.

From noon to 3:10 is \( 3\tfrac{1}{6} \) hours:

\[ 3\tfrac{1}{6} \times 30 = 95^{\circ} \]

The extra ten minutes contribute \( 10 \times 0.5 = 5^{\circ} \), which is what lifts the answer above the whole-hour figure.

Answer: C

Time from 9 a.m. to 4 p.m. = 7 hrs
The clock gains 5 secs in 3 min
In 60 min, it will gain, (60 x 5) / 3 = 100 sec
i.e. the clock gains 100 seconds in one hour
In 7 hours, it will gain 700 sec.
700/60 mins = (11)2/3 mins

Answer: D

At 4 o’ clock, the hour hand is at 120° from the vertical.
In 15 minutes,
Hour hand = 120 + 15 x (0.5) = 120 + 7.5 = 127.5° (The hour hand moves at 0.5 dpm)
Minute hand = 15 x (6) = 90° (The minute hand moves at 6 dpm)
Difference or Angle between the hands = 127.5 - 90 = 37.5°

Answer: D

The hour hand sweeps the full \( 360^{\circ} \) in twelve hours, so it turns \( 30^{\circ} \) an hour.

\[ 6 \text{ hours} \times 30^{\circ} = 180^{\circ} \]

Only the hour hand is asked about; the minute hand would have turned \( 6 \times 360^{\circ} \) over the same period.

Answer: B

In each twelve-hour period the hands are at right angles 22 times - twice in most hours, but the crossings near 3 and 9 o'clock overlap so that two are lost.

\[ 22 \times 2 = 44 \text{ times in 24 hours} \]

The count is not 48, because between 2–3 and 3–4 (and again around 9) one right angle is shared rather than occurring twice.

Answer: A

In twelve hours the hands coincide eleven times, not twelve: between 11 and 12 they meet only at 12 o'clock itself, so that hour contributes no separate coincidence.

\[ 11 \times 2 = 22 \text{ times in 24 hours} \]

Equivalently, the minute hand laps the hour hand once every \( \tfrac{720}{11} = 65\tfrac{5}{11} \) minutes, and \( \tfrac{1440}{720/11} = 22 \).

Answer: D

The hour hand sweeps the full \( 360^{\circ} \) in twelve hours, so it turns \( 30^{\circ} \) an hour.

\[ 6 \text{ hours} \times 30^{\circ} = 180^{\circ} \]

Only the hour hand is asked about; the minute hand would have turned \( 6 \times 360^{\circ} \) over the same period.

Answer: C

The hour hand turns \( 30^{\circ} \) an hour, or \( 0.5^{\circ} \) a minute.

From noon to 5:10 is \( 5\tfrac{1}{6} \) hours:

\[ 5\tfrac{1}{6} \times 30 = 155^{\circ} \]

The extra ten minutes contribute \( 10 \times 0.5 = 5^{\circ} \), which is what lifts the answer above the whole-hour figure.

Answer: B

The hour hand moves \( 0.5^{\circ} \) a minute and the minute hand \( 6^{\circ} \), so at \( H \) hours \( M \) minutes the angle between them is

\[ \theta = \left| 30H - 5.5M \right| \]

\[ \theta = \left| 30(4) - 5.5(20) \right| = \left| 120 - 110 \right| = 10^{\circ} \]

The minute hand is at the 4, and the hour hand has drifted a third of the way past it - \( 20 \times 0.5 = 10^{\circ} \) - which is exactly the gap.