Clocks Questions and Answers

Answer: B

A mirror reverses the dial, so a reading of \( T \) appears as \( 12{:}00 - T \) (or \( 11{:}60 - T \), which is easier to subtract).

\[ 11{:}60 - 11{:}25 = 0{:}35 \quad\Longrightarrow\quad 12{:}35 \]

Checking: 12:35 seen in a mirror does show 11:25, since the two are equally far either side of the 12.

Answer: D

Correct answer: 44

The hands lie in a straight line when they coincide and when they are opposite. Each happens 11 times in 12 hours, giving 22 in twelve hours.

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

The count is 44 rather than 48 because the minute hand laps the hour hand only 11 times in 12 hours, not 12.

Answer: A

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

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

A right angle means \( \theta = 90 \), with \( H = 9 \):

\[ \left| 270 - 5.5M \right| = 90 \]

\[ 5.5M = 180 \quad\text{or}\quad 5.5M = 360 \]

\[ M = \frac{360}{11} = 32\tfrac{8}{11} \quad\text{or}\quad M = 65\tfrac{5}{11} \text{ (past the hour)} \]

So the first right angle after 9 am comes at \( 32\tfrac{8}{11} \) minutes past 9.

Answer: A

Time from 5 am. on a day to 10 pm. on 4th day = 89 hours.

Now 23 hrs 44 min. of this clock = 24 hours of correct clock.

356/15 hrs of this clock = 24 hours of correct clock

89 hrs of this clock = (24 x 31556 x 89) hrs of correct clock.

= 90 hrs of correct clock.

So, the correct time is 11 p.m.

Answer: C

At 3 o'clock, the hands of the watch are 15 min. space apart.
To be in opposite directions, they must be 30 min. spaces apart. 
Minute hand must gain 45 min. space (15 + 30 min)
55 min spaces are gained in 60 min. 
45 min. spaces would be gained in (60/55 × 45) min.
Required time = 49 1/11 min. past 3.

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

At 2 o’ clock, the hour hand is at 60° from the vertical.
In 40 minutes,
Hour hand = 60 + 40 x (0.5) = 80° (The hour hand moves at 0.5 dpm)
Minute hand = 40 x (6) = 240° (The minute hand moves at 6 dpm)
Difference or angle between the hands = 240 - 80 = 160°

Answer: D

Correct answer: 2:25 p.m.

From 8 a.m. to 3 p.m. is 7 true hours, and the watch loses 5 minutes in each of them.

\[\text{Total loss} = 7 \times 5 = 35 \text{ minutes}\]

The watch therefore reads 35 minutes behind the true time, showing 2:25 p.m. when the correct time is 3 p.m.

Answer: C

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: 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

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

\[ \theta = \left| 30(5) - 5.5(15) \right| = \left| 150 - 82.5 \right| \]

\[ = 67.5^{\circ} \]

The minute hand sits on the 3 and the hour hand a quarter of the way past the 5, so the gap is a little under the \( 60^{\circ} \) between the 3 and the 5.