Clock Test questions are a common type of problem in the logical reasoning section of competitive exams in India. They test a candidate's understanding of the movement and relationship between the hands of a clock (hour, minute, and sometimes second). Solving these requires knowledge of angles, relative speed, and time calculations.
0.5° per minute
.6° per minute
.5.5° per minute
.θ = | (11/2) * M - 30 * H |
Note: H is the hour (1-12), M is the minute (0-59). The result is the smaller angle. The reflex angle is 360° - θ.
11:60
(or 12:00
). For times involving seconds, subtract from 11:59:60
.Question: What is the angle between the minute hand and the hour hand of a clock at 3:30?
A) 60°
B) 75°
C) 90°
D) 105°
Answer: B) 75°
Technique: Use the standard angle formula.
Formula: Angle = | (11/2) * M - 30 * H |
Here, H = 3, M = 30.
Angle = | (11/2) * 30 - 30 * 3 | = | 165 - 90 | = 75°.
Diagram Angle Calculation:
- Minute Hand: 30 mins * 6°/min = 180° from 12.
- Hour Hand: (3 hrs * 30°) + (30 mins * 0.5°) = 90° + 15° = 105° from 12.
Question: At what time between 4 and 5 o'clock will the hands of a clock be together (coincide)?
A) 4:20
B) 4:21 9/11
C) 4:22 8/11
D) 4:23 7/11
Answer: B) 4:21 9/11
Technique: Use the relative speed concept. For the hands to coincide, the minute hand has to gain the initial angle gap between them.
At 4 o'clock, the hour hand is at 4 and the minute hand is at 12. The gap is 20 minute spaces.
Initial angle gap = 4 * 30° = 120°.
The minute hand gains 5.5° per minute. Time required = Total Angle to Gain / Relative Speed
Time = 120° / 5.5° = 120 / (11/2) = 240 / 11 = 21 9/11 minutes.
So, the hands will coincide at 21 9/11 minutes past 4.
Question: A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours. What will be the true time when the clock indicates 1 p.m. on the following day?
A) 12:48 p.m.
B) 12 p.m.
C) 1 p.m.
D) 11:48 a.m.
Answer: A) 12:48 p.m.
Technique: Calculate the ratio of correct time to incorrect time.
The incorrect clock gains 10 minutes in 24 hours. This means:
24 hours 10 minutes of the incorrect clock = 24 hours of the correct clock.
(24 + 10/60) hrs of incorrect clock = 24 hrs of correct clock.
(145/6) hrs of incorrect clock = 24 hrs of correct clock.
Time elapsed on the incorrect clock from 8 a.m. (Day 1) to 1 p.m. (Day 2) = 29 hours.
If (145/6) incorrect hours = 24 correct hours, then 29 incorrect hours = ?
Correct hours = 29 * (24 / (145/6)) = 29 * (24 * 6 / 145) = (29 * 144) / (29 * 5) = 144 / 5 = 28.8 hours.
28.8 hours = 28 hours and 0.8 * 60 minutes = 28 hours and 48 minutes.
The true time is 28 hours and 48 minutes after 8 a.m. (Day 1).
8 a.m. (Day 1) + 24 hours = 8 a.m. (Day 2).
8 a.m. (Day 2) + 4 hours 48 minutes = 12:48 p.m.
Question: The reflection of a wall clock in a mirror shows the time as 3:40. What is the actual time?
A) 8:20
B) 9:20
C) 8:40
D) 9:40
Answer: A) 8:20
Technique: Subtract the mirror time from 11:60.
11 : 60
- 03 : 40
-----------
08 : 20
The actual time is 8:20.
Question: What is the reflex angle between the hands of a clock at 10:25?
A) 162.5°
B) 180°
C) 197.5°
D) 192.5°
Answer: C) 197.5°
Technique: First find the smaller angle using the formula, then subtract it from 360° to get the reflex angle.
Step 1: Find the smaller angle.
H = 10, M = 25. Angle = | (11/2) * 25 - 30 * 10 | = | 137.5 - 300 | = 162.5°.
Step 2: Find the reflex angle.
Reflex Angle = 360° - 162.5° = 197.5°.
Question 6: At what time between 7 and 8 o'clock are the hands at an angle of 45°?
A) 7:30 and 7:46 4/11
B) 7:30 and 7:43 7/11
C) 7:30 and 7:40 10/11
D) 7:30 and 7:45
Answer: A) 7:30 and 7:46 4/11
Using M = (2/11)(30H ± θ)
with H=7, θ=45.
Case 1 (Hour hand ahead): M = (2/11)(210 - 45) = 330/11 = 30 min. Time is 7:30.
Case 2 (Minute hand ahead): M = (2/11)(210 + 45) = 510/11 = 46 4/11 min. Time is 7:46 4/11.
Question 7: How many times in a day are the hands of a clock in a straight line but opposite in direction?
A) 11
B) 22
C) 24
D) 44
Answer: B) 22
The hands of a clock are opposite (180°) once every hour, except in the interval between 5 and 7, where it happens only once at 6 o'clock.
This means they are opposite 11 times in 12 hours.
In a full day (24 hours), they will be opposite 11 * 2 = 22 times.
Question 8: A clock loses 5 minutes every hour and was set right at 6 a.m. on a Monday. When will it show the correct time again?
A) 6 days later, 6 a.m.
B) 5 days later, 6 p.m.
C) 6 days later, 6 p.m.
D) 7 days later, 6 a.m.
Answer: A) 6 days later, 6 a.m.
For a clock to show the correct time again, it must lose a full 12 hours.
12 hours = 12 * 60 = 720 minutes.
The clock loses 5 minutes in 1 hour.
Time required to lose 720 minutes = (720 minutes) / (5 minutes/hour) = 144 hours.
144 hours = 144 / 24 = 6 days.
So, the clock will show the correct time exactly 6 days after it was set.
It was set at 6 a.m. on Monday, so it will show the correct time at 6 a.m. on the following Sunday (which is 6 days later).
Question 9: What time is shown by the mirror if the actual time is 11:09?
A) 12:51
B) 1:51
C) 12:49
D) 1:49
Answer: A) 12:51
Subtract from 11:60.
11:60 - 11:09 = 00:51.
A time of 00 hours is interpreted as 12 in a 12-hour clock format.
So the time is 12:51.
Question 10: How many degrees does the hour hand move in 20 minutes?
A) 10°
B) 12°
C) 20°
D) 120°
Answer: A) 10°
The speed of the hour hand is 0.5° per minute.
In 20 minutes, the hour hand moves = 20 minutes * 0.5°/minute = 10°.
Question 11: At 4:20, the hour hand and the minute hand of a clock form an angle of:
A) 0°
B) 5°
C) 10°
D) 20°
Answer: C) 10°
Using the formula: H=4, M=20.
Angle = | (11/2)*20 - 30*4 | = | 110 - 120 | = |-10| = 10°.
Question 12: At what time between 9 and 10 o'clock will the hands of a clock be in a straight line, but not together?
A) 9:15
B) 9:16 4/11
C) 9:17 3/11
D) 9:18 2/11
Answer: B) 9:16 4/11
This means the hands are opposite (180°). At 9 o'clock, the angle is 270°. To be 180°, the minute hand must gain 270° - 180° = 90°.
Time = 90 / 5.5 = 90 / (11/2) = 180/11 = 16 4/11 minutes past 9.
Question 13: How many times are the hands of a clock at a right angle in a day?
A) 22
B) 24
C) 44
D) 48
Answer: C) 44
The hands are at a right angle (90°) twice every hour, except at 3 and 9 o'clock intervals where one opportunity is missed. This results in 22 right angles in 12 hours. In a full day (24 hours), there are 22 * 2 = 44 right angles.
Question 14: A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min 48 sec fast at 2 p.m. on the following Monday. When was it correct?
A) 2 p.m. on Tuesday
B) 2 p.m. on Wednesday
C) 3 p.m. on Thursday
D) 1 p.m. on Friday
Answer: B) 2 p.m. on Wednesday
From Monday noon to the next Monday 2 p.m. is 7 days and 2 hours = 170 hours.
Total time gained = 2 min (slow) + 4 min 48 sec (fast) = 6 min 48 sec = 6.8 minutes.
The watch gains 6.8 minutes in 170 hours.
To show the correct time, it must gain the initial 2 minutes it was slow.
Time to gain 2 minutes = (170 hours / 6.8 min) * 2 min = 50 hours.
The correct time will be shown 50 hours after Monday noon. 50 hours = 2 days and 2 hours.
Monday noon + 2 days = Wednesday noon. Wednesday noon + 2 hours = 2 p.m. on Wednesday.
Question 15: Find the time shown in the mirror if the actual time is 1:11:15 (Hr:Min:Sec).
A) 10:48:45
B) 10:49:45
C) 11:48:45
D) 11:49:45
Answer: A) 10:48:45
When seconds are involved, subtract the time from 11:59:60.
11h 59m 60s - 1h 11m 15s = 10h 48m 45s.
Question 16: The angle between the hands of a clock at 12:30 is:
A) 165°
B) 180°
C) 195°
D) 150°
Answer: A) 165°
For 12:30, use H=0 in the formula for simplicity.
Angle = | (11/2)*30 - 30*0 | = | 165 - 0 | = 165°.
Question 17: At what time between 2 and 3 o'clock will the hands of a clock be at a right angle?
A) 2:27 3/11
B) 2:30
C) 2:25 5/11
D) 2:28 2/11
Answer: A) 2:27 3/11
Using M = (2/11)(30H ± 90). H=2.
Case 1 (Hour hand ahead, angle < 90): M = (2/11)(60 - 90) = Negative. Ignore. The minute hand has to pass the hour hand.
Case 2 (Minute hand ahead): M = (2/11)(60 + 90) = (2/11)(150) = 300/11 = 27 3/11 minutes past 2.
Question 18: A clock is 5 minutes fast. If the clock shows 10:10 a.m., what is the correct time?
A) 10:00 a.m.
B) 10:05 a.m.
C) 10:15 a.m.
D) 9:55 a.m.
Answer: B) 10:05 a.m.
The clock is running fast, so the time it shows is ahead of the actual time. To find the correct time, we must subtract the extra minutes.
Correct Time = Shown Time - Gained Time = 10:10 - 5 minutes = 10:05 a.m.
Question 19: How much time does the minute hand take to gain 12 degrees over the hour hand?
A) 2 minutes
B) 2 2/11 minutes
C) 3 minutes
D) 3 3/11 minutes
Answer: B) 2 2/11 minutes
The relative speed of the minute hand over the hour hand is 5.5° per minute.
Time = Angle to gain / Relative speed = 12° / 5.5° = 12 / (11/2) = 24 / 11 = 2 2/11 minutes.
Question 20: A man looks at a mirror and sees the clock showing 8:50. What is the correct time?
A) 3:10
B) 4:10
C) 3:50
D) 4:50
Answer: A) 3:10
Subtract from 11:60.
11:60 - 8:50 = 3:10.
Question 21: Find the angle between the hands of a clock at 8:20.
A) 120°
B) 130°
C) 140°
D) 150°
Answer: B) 130°
Angle = | (11/2)*20 - 30*8 | = | 110 - 240 | = |-130| = 130°.
Question 22: At what time between 1 and 2 o'clock will the hands be opposite to each other?
A) 1:35 5/11
B) 1:36 6/11
C) 1:37 7/11
D) 1:38 2/11
Answer: D) 1:38 2/11
At 1 o'clock, the minute hand has to gain 30° (to catch up) + 180° (to go opposite) = 210°.
Time = 210 / 5.5 = 210 / (11/2) = 420/11 = 38 2/11 minutes past 1.
Question 23: A clock strikes once at 1 o'clock, twice at 2 o'clock, and so on. How many times will it strike in 24 hours?
A) 78
B) 156
C) 180
D) 196
Answer: B) 156
The number of strikes in 12 hours is the sum of the first 12 natural numbers: 1+2+3+...+12.
Sum = n(n+1)/2 = 12(13)/2 = 78.
In 24 hours, this cycle repeats.
Total strikes = 78 * 2 = 156.
Question 24: The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of the correct time. How much does the clock gain or lose in a day?
A) Gains 10 10/143 min
B) Loses 10 10/143 min
C) Gains 11 min
D) Loses 11 min
Answer: A) Gains 10 10/143 min
In a correct clock, the hands coincide every 65 5/11 minutes.
This clock's hands coincide every 65 minutes. It is faster than the correct clock, so it gains time.
Gain in 65 minutes = (65 5/11) - 65 = 5/11 minutes.
In 65 minutes of incorrect time, the clock gains 5/11 min.
In 1 day (24 hours = 1440 minutes), the gain is (5/11 * 1/65) * 1440 = (1/143) * 1440 = 10 10/143 minutes.
Question 25: What is the angle traced by the hour hand in 2 hours and 30 minutes?
A) 60°
B) 75°
C) 90°
D) 105°
Answer: B) 75°
Total time in minutes = 2 * 60 + 30 = 150 minutes.
Speed of hour hand = 0.5° per minute.
Angle traced = 150 * 0.5 = 75°.
Question 26: At 5:15, what is the smaller angle between the clock hands?
A) 60°
B) 62.5°
C) 65°
D) 67.5°
Answer: D) 67.5°
Angle = | (11/2)*15 - 30*5 | = | 82.5 - 150 | = |-67.5| = 67.5°.
Question 27: How many times between 4 PM and 10 PM do the hands of a clock coincide?
A) 5
B) 6
C) 7
D) 8
Answer: B) 6
Hands coincide once per hour. The intervals are 4-5, 5-6, 6-7, 7-8, 8-9, 9-10. This gives a total of 6 times.
Question 28: My watch, which was correct at noon, shows 5:10 PM when the correct time is 5 PM. How many minutes does my watch gain per hour?
A) 1 min
B) 1.5 min
C) 2 min
D) 2.5 min
Answer: C) 2 min
From noon to 5 PM, the correct clock has passed 5 hours. In these 5 hours, the incorrect watch has gained 10 minutes. Gain per hour = Total Gain / Total Hours = 10 min / 5 hours = 2 minutes per hour.
Question 29: What time does a mirror show if the real time is 6:00?
A) 6:00
B) 12:00
C) 5:00
D) 7:00
Answer: A) 6:00
A vertical reflection of 6:00 is still 6:00. Using the formula: 12:00 - 6:00 = 6:00.
Question 30: At what angle are the hands of a clock inclined at 15 minutes past 5?
A) 67.5°
B) 72.5°
C) 58.5°
D) 64°
Answer: A) 67.5°
This is the same as Question 26, asking for the angle at 5:15. Angle = 67.5°.
Question 31: How many degrees will the minute hand move in the same time in which the hour hand moves 6°?
A) 60°
B) 72°
C) 84°
D) 90°
Answer: B) 72°
The hour hand moves at 0.5°/min. Time taken to move 6° = 6 / 0.5 = 12 minutes. The minute hand moves at 6°/min. In 12 minutes, it moves = 12 * 6 = 72°.
Question 32: At what time between 5:30 and 6:00 will the hands of a clock be at right angles?
A) 5:40
B) 5:43 7/11
C) 5:45
D) 5:50
Answer: B) 5:43 7/11
Using M = (2/11)(30H ± 90) for H=5. We need a value between 30 and 60.
Case 1 (-): M = (2/11)(150 - 90) = 120/11 = 10 10/11. (Not in range)
Case 2 (+): M = (2/11)(150 + 90) = 480/11 = 43 7/11 minutes past 5. (This is in the range).
Question 33: A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:
A) 145°
B) 150°
C) 155°
D) 160°
Answer: C) 155°
From noon to 5:10 is 5 hours and 10 minutes. Total minutes = 5 * 60 + 10 = 310 minutes. Hour hand speed = 0.5°/min. Angle turned = 310 * 0.5 = 155°.
Question 34: What is the time in a mirror if the clock shows 12:20?
A) 11:40
B) 12:40
C) 1:40
D) 2:40
Answer: A) 11:40
12:xx is tricky. Treat 12 as 0. Subtract 0:20 from 11:60. 11:60 - 0:20 = 11:40. Alternatively, subtract 12:20 from 23:60 (or 24:00). 23:60 - 12:20 = 11:40.
Question 35: Angle at 7:35?
A) 15°
B) 16.5°
C) 17.5°
D) 18.5°
Answer: C) 17.5°
Angle = | (11/2)*35 - 30*7 | = | 192.5 - 210 | = |-17.5| = 17.5°.
Question 36: How many times do the hands of a clock coincide in a day?
A) 11
B) 12
C) 22
D) 24
Answer: C) 22
The hands coincide once every hour, but only once between 11 and 1 (at 12 o'clock). This means they coincide 11 times in 12 hours. In a day (24 hours), they coincide 11 * 2 = 22 times.
Question 37: A clock is 10 minutes slow. If it shows 6:00 p.m., what is the actual time?
A) 5:50 p.m.
B) 6:10 p.m.
C) 6:00 p.m.
D) 6:05 p.m.
Answer: B) 6:10 p.m.
The clock is slow, meaning it is behind the actual time. To get the correct time, we must add the lost time. Correct Time = Shown Time + Lost Time = 6:00 + 10 minutes = 6:10 p.m.
Question 38: Angle at 2:40?
A) 150°
B) 160°
C) 170°
D) 180°
Answer: B) 160°
Angle = | (11/2)*40 - 30*2 | = | 220 - 60 | = 160°.
Question 39: At what time between 3 and 4 o'clock are the hands 4 minutes apart?
A) 3:12
B) 3:15
C) 3:20 8/11
D) 3:24
Answer: A) 3:12 and C) 3:20 8/11
Angle = 4 min * 6°/min = 24°.
M=(2/11)(30*3 ± 24).
Case 1: M=(2/11)(90-24) = 132/11 = 12 min. Time is 3:12.
Case 2: M=(2/11)(90+24) = 228/11 = 20 8/11 min. Time is 3:20 8/11.
Question 40: Time in mirror is 12:30. Actual time?
A) 11:30
B) 12:30
C) 1:30
D) 6:30
Answer: A) 11:30
Subtract from 23:60 for 24-hour cycle. 23:60 - 12:30 = 11:30. Or, from 11:60, treating 12 as 0. 11:60 - 0:30 = 11:30.
Question 41: Angle at 6:45?
A) 60°
B) 62.5°
C) 65°
D) 67.5°
Answer: D) 67.5°
Angle = | (11/2)*45 - 30*6 | = | 247.5 - 180 | = 67.5°.
Question 42: A clock takes 6 seconds to strike 4 times. How long will it take to strike 10 times?
A) 15 seconds
B) 18 seconds
C) 21 seconds
D) 24 seconds
Answer: B) 18 seconds
To strike 4 times, there are 3 intervals between the strikes. Time per interval = 6 seconds / 3 intervals = 2 seconds. To strike 10 times, there are 9 intervals. Total time = 9 intervals * 2 seconds/interval = 18 seconds.
Question 43: Angle at 1:05?
A) 2.5°
B) 5°
C) 1.5°
D) 0°
Answer: A) 2.5°
Angle = | (11/2)*5 - 30*1 | = | 27.5 - 30 | = |-2.5| = 2.5°.
Question 44: The minute hand moves through an angle of _____ in one minute.
A) 0.5°
B) 1°
C) 6°
D) 12°
Answer: C) 6°
The minute hand covers 360° in 60 minutes. So, in one minute, it covers 360/60 = 6°.
Question 45: If a clock shows 3:14, what is the mirror image?
A) 8:46
B) 9:46
C) 8:56
D) 9:56
Answer: A) 8:46
11:60 - 3:14 = 8:46.
Question 46: When are the hands of a clock 16 minute spaces apart between 3 and 4 o'clock?
A) 3:00
B) 3:30
C) 3:33 9/11
D) 3:40
Answer: C) 3:33 9/11
Angle = 16 min * 6°/min = 96°. M = (2/11)(30*3 + 96) because the minute hand has to be ahead. M = (2/11)(90+96) = (2/11)(186) = 372/11 = 33 9/11 minutes past 3.
Question 47: A clock gains 15 minutes in a day (24 hours). If it is set correctly at 12 noon, what time will it show at 4 AM the next day?
A) 4:10 AM
B) 4:15 AM
C) 4:20 AM
D) 4:05 AM
Answer: A) 4:10 AM
Time from 12 noon to 4 AM next day = 16 hours. The clock gains 15 min in 24 hours. Gain in 16 hours = (15/24) * 16 = 10 minutes. The clock will show 4:00 AM + 10 minutes = 4:10 AM.
Question 48: At 9:00, the angle between the hands is 90°. What is the reflex angle?
A) 90°
B) 180°
C) 270°
D) 360°
Answer: C) 270°
The smaller angle at 9:00 is 90°. The reflex angle is 360° - 90° = 270°.
Question 49: An accurate clock shows 7 a.m. Through how many degrees will the hour hand rotate when the clock shows 1 p.m.?
A) 150°
B) 180°
C) 160°
D) 120°
Answer: B) 180°
Time elapsed from 7 a.m. to 1 p.m. is 6 hours. The hour hand moves 30° in one hour. Total rotation = 6 hours * 30°/hour = 180°.
Question 50: What is the angle between the two hands of a clock when the time is 8:30?
A) 60°
B) 75°
C) 80°
D) 90°
Answer: B) 75°
Angle = | (11/2)*30 - 30*8 | = | 165 - 240 | = |-75| = 75°.