Pariksha SaathiReasoning
Clock: Practice Questions with Answers
19 practice questions on Clock, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.
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Q.1
Find the angle between the hour and minute hands at 3:00.
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Answer: 90°
Solution:
- Hour-hand angle = 30 × 3 + 0.5 × 0 = 90°. Minute-hand angle = 6 × 0 = 0°.
- Difference = |90 − 0| = 90°.
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Q.2
At what time between 4 and 5 o'clock will the hour and minute hands coincide (overlap exactly)?
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Answer: 4:21 9/11 (21 9/11 minutes past 4)
Solution:
- Hour-hand angle at M minutes past 4 = 120 + 0.5M. Minute-hand angle = 6M.
- For the hands to coincide, set them equal: 6M = 120 + 0.5M → 5.5M = 120 → M = 120/5.5 = 240/11 = 21 9/11.
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Q.3
At what time between 9 and 10 o’clock will the hour and minute hands be exactly opposite each other (180° apart)?
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Answer: 9:16 4/11 (16 4/11 minutes past 9)
Solution:
- Hour-hand angle at M minutes past 9 = 270 + 0.5M. Minute-hand angle = 6M.
- For the hands to be opposite, the hour hand (still ahead at this point in the hour) must lead the minute hand by 180°: (270 + 0.5M) − 6M = 180 → 270 − 5.5M = 180 → 5.5M = 90 → M = 90/5.5 = 180/11 ≈ 16.36.
- So the hands are opposite at 9 hours and 180/11 minutes, i.e., 16 4/11 minutes past 9.
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Q.4
Find the angle between the hour and minute hands at 4:30.
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Answer: 45°
Solution:
- Hour-hand angle = 30 × 4 + 0.5 × 30 = 120 + 15 = 135°. Minute-hand angle = 6 × 30 = 180°.
- Difference = |135 − 180| = 45°.
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Q.5
The reflection of a clock in a mirror shows the time as 4:20. What is the actual time?
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Answer: 7:40
Solution:
- Actual time = 11:60 − mirror time.
- 11:60 − 4:20 = 7:40.
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Q.6
Find the angle between the hour and minute hands at 7:20.
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Answer: 100°
Solution:
- Hour-hand angle = 30 × 7 + 0.5 × 20 = 210 + 10 = 220°. Minute-hand angle = 6 × 20 = 120°.
- Difference = |220 − 120| = 100°.
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Q.7
At what time between 3 and 4 o'clock, after 3:00 itself, will the hands next be at right angles (90° apart)?
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Answer: 3:32 8/11 (32 8/11 minutes past 3)
Solution:
- At 3:00 exactly, the hands are already 90° apart (hour ahead). As the minute hand gains on the hour hand, this gap shrinks to 0 (coincide) and then grows again with the minute hand now ahead.
- The NEXT right angle happens when the minute hand is 90° ahead of the hour hand: 6M − (90 + 0.5M) = 90 → 5.5M = 180 → M = 180/5.5 = 360/11 = 32 8/11.
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Q.8
At what time between 2 and 3 o’clock will the hour and minute hands be exactly opposite each other (180° apart)?
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Q.9
Find the angle between the hour and minute hands at 10:10.
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Answer: 115°. Hour = 305°, minute = 60°, difference 245°, which is more than 180° so use 360−245.
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Q.10
Find the angle between the hour and minute hands at 6:00.
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Q.11
The reflection of a clock in a mirror shows the time as 5:40. What is the actual time?
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Q.12
Find the angle between the hour and minute hands at 2:40.
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Q.13
At what time between 7 and 8 o'clock will the hour and minute hands coincide?
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Q.14
At what time between 5 and 6 o'clock will the hands FIRST be at right angles after 5:00?
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Answer: 5:10 10/11. The hour hand starts 150° ahead; it shrinks to 90° ahead first (the later 90°-ahead-the-other-way case happens afterward, at 5:43 7/11).
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Q.15
In a 24-hour day, how many times are the hour and minute hands of a clock at right angles (90°) to each other?
- A 44
- B 22
- C 24
- D 48
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Correct answer: (A) 44
The hands are at right angles twice as often as they coincide — 22 coincidences in 24 hours means 44 right-angle moments in 24 hours.
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Q.16
A clock loses 5 minutes every hour. If it is set correctly at 12:00 noon, what time will it show at 8:00 pm the same day (8 hours later)?
- A 7:20
- B 7:25
- C 7:30
- D 7:15
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Correct answer: (A) 7:20
In 8 hours the clock loses 5×8 = 40 minutes, so it shows 7:20 instead of the correct 8:00.
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Q.17
How many times do the hour and minute hands of a clock coincide (come together) in a 24-hour day?
- A 22
- B 24
- C 23
- D 11
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Correct answer: (A) 22
The hands coincide 11 times in every 12-hour period (not 12, because the coincidence at the very start and the very end of the 12 hours is the same instant), so in 24 hours they coincide 22 times.
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Q.18
A clock gains 5 minutes every hour. It is set to the correct time at 12:00 noon. What time will it show when the actual time is 4:00 pm?
- A 4:20 pm
- B 4:00 pm
- C 4:25 pm
- D 4:15 pm
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Correct answer: (A) 4:20 pm
In 4 actual hours (240 minutes), a clock that gains 5 min/hour advances 65 clock-minutes for every 60 actual minutes: 240 × (65/60) = 260 clock-minutes = 4 hours 20 minutes. Starting from 12:00, it shows 4:20 pm.
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Q.19
In a 12-hour period, how many times do the hour and minute hands together form a straight line (either exactly together or exactly opposite)?
- A 22
- B 11
- C 24
- D 44
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Correct answer: (A) 22
The hands coincide 11 times and are exactly opposite 11 times in every 12-hour period — 11 + 11 = 22 straight-line moments in total.
How these questions were made
Written by Mahesh Srivastava, Founder of Pariksha Saathi. Published: 2026-10-03.
Authored by an AI assistant (Claude) - not reviewed by a subject-matter expert.