Clocks Questions and Answers

Answer: D

Correct answer: 22

In each hour the hands are normally at right angles twice, which would suggest 24 in twelve hours. But between 2 and 3, and again between 8 and 9, one of those positions falls outside the hour, so two are lost, giving 22.

Equivalently, the minute hand gains \(360°\) on the hour hand 11 times in 12 hours, and each gain produces two right angles: \(11 \times 2 = 22\).

Answer: B

Time from 5 am On a day to 3 pm on 8th day = 178 hours
Now 23 hrs 44 min. of this clock = 24 hours of correct clock
365/15 hrs of this clock = 24 hours of correct clock
178 hrs of this clock = (24 × 15/356 × 89) hrs of correct clock
= 180 hrs of correct clock.
So, the correct time is 5 pm.

Answer: D

55 min. spaces are covered in 60 min.
60 min. spaces are covered in (60/55 × 60) min = 65 5/11 min
Loss in 64 min = (65 5/11 - 64) = 16/11 min
Loss in 24 hrs= (16/11 × 1/64 × 24 × 60) min = 32 (8/11) min.

Answer: B

Correct answer: 315°

First find the ordinary angle between the hands.

\[\text{Hour hand} = 4 \times 30 + 30 \times 0.5 = 120 + 15 = 135°\]

\[\text{Minute hand} = 30 \times 6 = 180°\]

The hands are \(180 - 135 = 45°\) apart, so the reflex angle is

\[360 - 45 = 315°\]

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: B

The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock).

The hands overlap about every 65 minutes, not every 60 minutes.
Therefore, The hands coincide 22 times in a day.

Answer: D

Correct answer: 54 (6/11) min past 10

At 10 o’clock the hour hand leads the minute hand by \(300°\), and the minute hand gains \(5.5°\) per minute.

\[t = \frac{300}{5.5} = \frac{600}{11} = 54\tfrac{6}{11}\ \text{minutes}\]

So they coincide at \(54\tfrac{6}{11}\) minutes past 10, the last coincidence before the hands meet again at 12.

Answer: B

Correct answer: 100°

The hour hand covers \(360°\) in 12 hours, so it moves \(30°\) per hour, or \(0.5°\) per minute.

\[3 \times 30 + 20 \times 0.5 = 90 + 10 = 100°\]

The minute hand, by contrast, would sweep \(1200°\) in the same interval.

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: B

Correct answer: 11 p.m.

While the true time advances 1440 minutes, this clock advances only \(1440 - 16 = 1424\) minutes.

From 5 a.m. on the first day to 10 p.m. on the fourth is 3 days and 17 hours, or 89 hours, as shown by the clock. Scaling to true time:

\[89 \times \frac{1440}{1424} = 89 \times \frac{90}{89} = 90 \text{ hours}\]

Adding 90 hours to 5 a.m. gives 3 days and 18 hours later, which is 11 p.m. on the fourth day.