Clocks Questions and Answers

Answer: A

Time from 5am on a day to 10 pm on fourth day= 89 hours
Presently 23hrs. 44min. of this clock= 24 hours of right clock.
∴ 356/15 hrs of this clock= (24*15/356*89) hrs. Of right clock.
= 90 hrs of right clock.
Along these lines, the right time is 11 pm.

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

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.

Answer: D

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

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

\[ \theta = \left| 300 - 137.5 \right| = 162.5^{\circ} \]

The reflex angle is what is left of the full turn:

\[ 360 - 162.5 = 197.5^{\circ} = 197\tfrac{1}{2}^{\circ} \]

A reflex angle is by definition greater than \( 180^{\circ} \), so the smaller 162.5 cannot be the answer.

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: D

At 3 o'clock ,the moment hand is 15 min. spaces a section
Structure the hour hand. To be coincident,
it must pick up 15 min. spaces.
55 min. are picked up in 60 min.
15 min. are picked up in (60/55*15)min.=180/11 min.
∴ The hands are correspondent at 180/11 min. past 3.

Answer: B

Time structure 12 p.m. on Monday to 2 p.m. on the accompanying
Monday =7 days 2 hours =170 hours.
∴ The watch gains(2+24/5)min.
on the other hand 34/5 min. in 170 hrs.
Now,34/5 min. are picked up in 170 hrs.
∴ 2 min. are picked up in (170(5/34*2) hrs=50 hrs.
Along these lines, the watch is right 2 days 2 hour after 12 p.m. on
Monday i.e.it will be right at 2 p.m. on Wednesday.

Answer: A

Correct answer: 10 (10/11) min past 2

At 2 o’clock the hour hand is \(60°\) ahead of the minute hand. The minute hand gains \(6 - 0.5 = 5.5°\) each minute, so it closes the gap in

\[t = \frac{60}{5.5} = \frac{120}{11} = 10\tfrac{10}{11}\ \text{minutes}\]

So the hands coincide at \(10\tfrac{10}{11}\) minutes past 2.

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: B

Correct answer: 95°

Measure both hands from the 12 o’clock mark.

\[\text{Hour hand} = 5 \times 30 + 10 \times 0.5 = 150 + 5 = 155°\]

\[\text{Minute hand} = 10 \times 6 = 60°\]

\[\text{Angle} = 155 - 60 = 95°\]

Answering \(90°\) ignores the \(5°\) the hour hand has moved past the 5.