Episode 8 — Aptitude and Reasoning / 8.19 — Clocks

8.19 Clocks - Practice MCQs

Instructions

Choose the best answer from options (a), (b), (c), (d).
Answers with explanations are provided at the end of each question.

Q1. The angle between the hands of a clock at 3:00 is:

(a) 60 degrees (b) 75 degrees (c) 90 degrees (d) 120 degrees

Answer: (c) 90 degrees

Angle = |30(3) - 5.5(0)| = 90 degrees

Q2. The angle between the hands at 6:00 is:

(a) 150 degrees (b) 160 degrees (c) 170 degrees (d) 180 degrees

Answer: (d) 180 degrees

Angle = |30(6) - 5.5(0)| = 180 degrees

Q3. What is the angle at 5:30?

(a) 10 degrees (b) 15 degrees (c) 20 degrees (d) 25 degrees

Answer: (b) 15 degrees

Angle = |30(5) - 5.5(30)| = |150 - 165| = 15 degrees

Q4. What is the angle at 8:20?

(a) 120 degrees (b) 125 degrees (c) 130 degrees (d) 135 degrees

Answer: (c) 130 degrees

Angle = |30(8) - 5.5(20)| = |240 - 110| = 130 degrees

Q5. At what time between 4 and 5 do the hands overlap?

(a) 4:20 (b) 4:21 and 9/11 min (c) 4:22 (d) 4:25

Answer: (b) 4:21 and 9/11 min

M = 60*4/11 = 240/11 = 21 + 9/11 minutes

Q6. How many times do the hands of a clock coincide in 24 hours?

(a) 20 (b) 22 (c) 24 (d) 11

Answer: (b) 22

11 times in 12 hours, so 22 times in 24 hours.

Q7. How many times are the hands at right angles in 12 hours?

(a) 11 (b) 22 (c) 24 (d) 44

Answer: (b) 22

The hands form right angles 22 times in 12 hours.

Q8. The minute hand moves how many degrees per minute?

(a) 3 degrees (b) 4 degrees (c) 5 degrees (d) 6 degrees

Answer: (d) 6 degrees

360 degrees / 60 minutes = 6 degrees per minute

Q9. The hour hand moves how many degrees per minute?

(a) 0.5 degrees (b) 1 degree (c) 1.5 degrees (d) 2 degrees

Answer: (a) 0.5 degrees

360 degrees / 720 minutes = 0.5 degrees per minute

Q10. The relative speed of the minute hand over the hour hand is:

(a) 5 degrees/min (b) 5.5 degrees/min (c) 6 degrees/min (d) 4.5 degrees/min

Answer: (b) 5.5 degrees/min

6 - 0.5 = 5.5 degrees per minute

Q11. At what time between 2 and 3 do the hands make an angle of 0 degrees?

(a) 2:10 and 10/11 min (b) 2:11 (c) 2:10 (d) 2:12

Answer: (a) 2:10 and 10/11 min

M = 60*2/11 = 120/11 = 10 + 10/11 minutes

Q12. At what time between 5 and 6 are the hands at 180 degrees?

(a) 5:54 and 6/11 min (b) 5:55 (c) 5:50 (d) 6:00

Answer: (a) 5:54 and 6/11 min

30(5) - 5.5M = -180
150 + 180 = 5.5M
M = 330/5.5 = 600/11 = 54 + 6/11 minutes

Q13. If a clock shows 2:15 in a mirror, the actual time is:

(a) 9:45 (b) 10:45 (c) 9:15 (d) 10:15

Answer: (a) 9:45

Actual = 11:60 - 2:15 = 9:45

Q14. If a clock shows 8:40 in a mirror, the actual time is:

(a) 3:20 (b) 4:20 (c) 3:40 (d) 4:40

Answer: (a) 3:20

Actual = 11:60 - 8:40 = 3:20

Q15. The angle traced by the minute hand in 20 minutes is:

(a) 100 degrees (b) 110 degrees (c) 120 degrees (d) 130 degrees

Answer: (c) 120 degrees

Angle = 6 * 20 = 120 degrees

Q16. The angle traced by the hour hand in 4 hours is:

(a) 60 degrees (b) 90 degrees (c) 120 degrees (d) 150 degrees

Answer: (c) 120 degrees

Angle = 30 * 4 = 120 degrees (or 0.5 * 240 = 120)

Q17. A clock gains 5 minutes every hour. If set at 12:00 noon, what does it show at 6:00 PM?

(a) 6:25 PM (b) 6:30 PM (c) 6:35 PM (d) 6:20 PM

Answer: (b) 6:30 PM

Real time = 6 hours = 360 minutes
Clock shows: 360 * 65/60 = 390 minutes = 6 hours 30 minutes
Clock shows 6:30 PM

Q18. A clock loses 4 minutes every hour. After how many days will it show the correct time?

(a) 7.5 days (b) 10 days (c) 15 days (d) 30 days

Answer: (a) 7.5 days

Loss per day = 4 * 24 = 96 minutes
Days to lose 12 hours (720 min) = 720/96 = 7.5 days

Q19. At what time between 7 and 8 are the hands at right angles?

(a) 7:21 and 9/11 min only (b) 7:21 and 9/11 min, and 7:54 and 6/11 min (c) 7:54 and 6/11 min only (d) 7:20 and 7:55

Answer: (b) 7:21 and 9/11 min, and 7:54 and 6/11 min

Case 1: M = (60*7 - 180)/11 = (420-180)/11 = 240/11 = 21 + 9/11 min
Case 2: M = (60*7 + 180)/11 = (420+180)/11 = 600/11 = 54 + 6/11 min
Both are between 0 and 60, so both valid.

Q20. The time between 2 consecutive overlaps of clock hands is:

(a) 60 minutes (b) 65 minutes (c) 65 and 5/11 minutes (d) 66 minutes

Answer: (c) 65 and 5/11 minutes

720/11 = 65 + 5/11 minutes

Q21. What is the angle at 12:30?

(a) 160 degrees (b) 165 degrees (c) 170 degrees (d) 175 degrees

Answer: (b) 165 degrees

Angle = |30(12) - 5.5(30)| = |360 - 165| = 195
Since 195 > 180: 360 - 195 = 165 degrees

Q22. What is the angle at 1:50?

(a) 105 degrees (b) 110 degrees (c) 115 degrees (d) 120 degrees

Answer: (c) 115 degrees

Angle = |30(1) - 5.5(50)| = |30 - 275| = 245
360 - 245 = 115 degrees

Q23. At what time between 6 and 7 do the hands overlap?

(a) 6:32 and 8/11 min (b) 6:30 (c) 6:33 (d) 6:35

Answer: (a) 6:32 and 8/11 min

M = 60*6/11 = 360/11 = 32 + 8/11 minutes

Q24. How many times in a day do the hands of a clock form a straight line (0 or 180)?

(a) 22 (b) 33 (c) 44 (d) 48

Answer: (c) 44

In 12 hours: 11 overlaps + 11 times at 180 = 22 straight lines
In 24 hours: 44

Q25. A clock shows 10:10. What is the angle?

(a) 110 degrees (b) 115 degrees (c) 120 degrees (d) 125 degrees

Answer: (b) 115 degrees

Angle = |30(10) - 5.5(10)| = |300 - 55| = 245
360 - 245 = 115 degrees

Q26. The mirror image of 5:25 is:

(a) 6:35 (b) 7:35 (c) 6:25 (d) 7:25

Answer: (a) 6:35

Actual (from mirror): 11:60 - 5:25 = 6:35
So the mirror image OF 5:25 shows 6:35 to the viewer.

Q27. At what time between 11 and 12 are the hands at 180 degrees?

(a) 11:54 and 6/11 min (b) 11:32 and 8/11 min (c) 11:40 (d) There is no such time

Answer: (a) 11:54 and 6/11 min

30(11) - 5.5M = -180
330 + 180 = 5.5M
M = 510/5.5 = 1020/11 = 92 + 8/11

That exceeds 60, so not valid for "between 11 and 12."

Let me try: 30(11) - 5.5M = 180
330 - 5.5M = 180
5.5M = 150
M = 150/5.5 = 300/11 = 27 + 3/11

So at 11:27 and 3/11 min. But that's not in the options either.

Hmm, let me reconsider. Between 11 and 12:
M = (60*11 - 360)/11 = (660-360)/11 = 300/11 = 27 + 3/11 min. -> 11:27 and 3/11

None of the options match. Let me check option (a):
54+6/11 = 600/11 which would be M = (60H+180)/11 with H=7: (420+180)/11=600/11. That's for 7.

For H=11: M=(660-360)/11 = 300/11 = 27.27 min.

The question and options don't align. Let me revise.

Revised: At what time between 11 and 12 do the hands form a straight line facing opposite directions (180 degrees)?

(a) 11:27 and 3/11 min (b) 11:30 (c) 11:35 (d) 11:40

Answer: (a) 11:27 and 3/11 min

M = (60*11 - 360)/11 = 300/11 = 27 + 3/11 minutes

Q28. A clock that gains 15 minutes per day will show the correct time again after:

(a) 24 days (b) 48 days (c) 72 days (d) 96 days

Answer: (b) 48 days

Days = 720/15 = 48 days

Q29. What is the reflex angle at 4:00?

(a) 120 degrees (b) 180 degrees (c) 240 degrees (d) 300 degrees

Answer: (c) 240 degrees

Normal angle at 4:00 = 120 degrees
Reflex = 360 - 120 = 240 degrees

Q30. At 12:00 noon, both hands coincide. The next time they coincide is:

(a) 1:00 (b) 1:05 and 5/11 min (c) 1:05 (d) 1:10

Answer: (b) 1:05 and 5/11 min

M = 60*1/11 = 60/11 = 5 + 5/11 minutes after 1:00
Or: 12:00 + 65 + 5/11 minutes = 1:05:27 approximately

Q31. The angle between the hands at 4:30 is:

(a) 30 degrees (b) 35 degrees (c) 40 degrees (d) 45 degrees

Answer: (d) 45 degrees

Angle = |30(4) - 5.5(30)| = |120 - 165| = 45 degrees

Q32. The angle at 9:15 is:

(a) 172.5 degrees (b) 175 degrees (c) 180 degrees (d) 177.5 degrees

Answer: (a) 172.5 degrees

Angle = |30(9) - 5.5(15)| = |270 - 82.5| = 187.5
360 - 187.5 = 172.5 degrees

Q33. How many times in a day do the hands of a clock overlap?

(a) 11 (b) 22 (c) 23 (d) 24

Answer: (b) 22

11 times in 12 hours, 22 in 24 hours.

Q34. At what time between 1 and 2 is the angle 60 degrees?

(a) 1:05 and 5/11 min, and 1:27 and 3/11 min (b) 1:10 and 1:30 (c) 1:16 and 4/11 min, and 1:27 and 3/11 min (d) 1:05 and 1:40

Answer: (c) 1:16 and 4/11 min, and 1:27 and 3/11 min

Case 1: M = (30 - 60)/5.5 = -30/5.5 < 0 (invalid)
Actually: M = (30*1 + 60)/5.5 = 90/5.5 = 180/11 = 16 + 4/11 min

Case 2: M = (30*1 - 60)/5.5 = -30/5.5 (negative, invalid)

Using the other form:
|30H - 5.5M| = 60
30 - 5.5M = 60 -> M = -30/5.5 (invalid)
30 - 5.5M = -60 -> 5.5M = 90 -> M = 90/5.5 = 180/11 = 16.36 min

For 60 degree, we also check:
5.5M - 30 = 60 -> M = 90/5.5 = 16 + 4/11 (same as above)
30 - 5.5M = 60 -> M < 0 (invalid)

Hmm, only one solution. Let me recheck:
At 1:00, angle = 30 degrees. The minute hand is catching up at 5.5 deg/min.
At some point, the gap is 60 degrees (ahead) and then 60 degrees (behind).

When minute hand is 60 degrees BEHIND hour hand: 30H - 5.5M = 60
30 - 5.5M = 60 -> M = -30/5.5 (negative: this was already past before 1:00)

When minute hand is 60 degrees AHEAD: 5.5M - 30H = 60
5.5M = 90, M = 180/11 = 16 + 4/11 min.

So only one solution between 1 and 2 for 60 degrees.

Actually wait, the minute hand overtakes at ~1:05. After that:
At some later time, the minute hand is 300 degrees ahead (or equivalently, hour hand is 60 degrees ahead again).
5.5M - 30 = 300 -> M = 330/5.5 = 60 (at 2:00, which is the boundary).

Hmm. So only 1 valid time. But the question expects 2 answers. Let me reconsider.

Actually, "angle of 60 degrees" can be either hand being ahead:
|30H - 5.5M| = 60 has TWO solutions in general:
30 - 5.5M = 60 -> M < 0 (invalid between 1-2)
30 - 5.5M = -60 -> M = 90/5.5 = 16 + 4/11

Only one solution. The question needs revision. Let me use angle = 54 degrees:
30 - 5.5M = 54 -> M = -24/5.5 (invalid)
30 - 5.5M = -54 -> M = 84/5.5 = 168/11 = 15 + 3/11

Still one solution. Let me try angle = 120:
30 - 5.5M = 120 -> M = -90/5.5 (invalid)
30 - 5.5M = -120 -> M = 150/5.5 = 300/11 = 27 + 3/11 min ✓

So for 120 degrees: only 27+3/11 min. One solution.

For two solutions between H and H+1, the angle must be < 30*H.
Between 1 and 2: angle < 30 degrees gives two solutions. Let me try 10 degrees:
30 - 5.5M = 10 -> M = 20/5.5 = 40/11 = 3 + 7/11 ✓
30 - 5.5M = -10 -> M = 40/5.5 = 80/11 = 7 + 3/11 ✓

Revised question with angle = 10 degrees:

Revised Q34: At what time between 1 and 2 is the angle between the hands 10 degrees?

(a) 1:03 and 7/11 min, and 1:07 and 3/11 min (b) 1:05 and 1:10 (c) 1:04 and 1:08 (d) 1:02 and 1:09

Answer: (a) 1:03 and 7/11 min, and 1:07 and 3/11 min

30 - 5.5M = 10 -> M = 20/5.5 = 40/11 = 3 + 7/11
30 - 5.5M = -10 -> M = 40/5.5 = 80/11 = 7 + 3/11

Q35. The angle between the hands at 2:20 is:

(a) 45 degrees (b) 50 degrees (c) 55 degrees (d) 60 degrees

Answer: (b) 50 degrees

Angle = |30(2) - 5.5(20)| = |60 - 110| = 50 degrees

Q36. If a clock shows 6:00, what time is seen in its mirror?

(a) 5:00 (b) 6:00 (c) 7:00 (d) 12:00

Answer: (b) 6:00

Mirror: 11:60 - 6:00 = 5:60 = 6:00
6:00 looks the same in a mirror.

Q37. At 3:40, the hour hand is at:

(a) 90 degrees from 12 (b) 100 degrees from 12 (c) 110 degrees from 12 (d) 120 degrees from 12

Answer: (c) 110 degrees from 12

Position = 30*3 + 0.5*40 = 90 + 20 = 110 degrees

Q38. A clock strikes 4 in 6 seconds. How long will it take to strike 8?

(a) 12 seconds (b) 14 seconds (c) 10 seconds (d) 16 seconds

Answer: (b) 14 seconds

For 4 strikes, there are 3 intervals. Time per interval = 6/3 = 2 seconds.
For 8 strikes, there are 7 intervals. Time = 7 * 2 = 14 seconds.

Q39. The angle between the hands at exactly 11:00 is:

(a) 30 degrees (b) 60 degrees (c) 90 degrees (d) 330 degrees

Answer: (a) 30 degrees

Angle = |30(11) - 5.5(0)| = 330 degrees
360 - 330 = 30 degrees (smaller angle)

Q40. Between 3 and 4, at what time are the hands in a straight line but not coinciding (180 degrees)?

(a) 3:49 and 1/11 min (b) 3:50 (c) 3:48 (d) 3:49 and 5/11 min

Answer: (a) 3:49 and 1/11 min

30(3) - 5.5M = -180
90 + 180 = 5.5M
M = 270/5.5 = 540/11 = 49 + 1/11 min

Q41. Two clocks are set correctly at noon. Clock A gains 3 min/hr and Clock B loses 2 min/hr. When will they show the same time?

(a) 120 hours (b) 144 hours (c) 160 hours (d) 180 hours

Answer: (b) 144 hours

Difference per hour = 3 + 2 = 5 minutes
Same time when difference = 720 minutes
Hours = 720/5 = 144 hours = 6 days

Q42. The angle at 12:20 is:

(a) 100 degrees (b) 110 degrees (c) 120 degrees (d) 130 degrees

Answer: (b) 110 degrees

Angle = |30(12) - 5.5(20)| = |360 - 110| = 250
360 - 250 = 110 degrees

Q43. How many degrees does the minute hand move in 1 hour?

(a) 180 degrees (b) 270 degrees (c) 360 degrees (d) 90 degrees

Answer: (c) 360 degrees

6 degrees/min * 60 min = 360 degrees (full rotation)

Next: 8.19 - Quick Revision