Free Topic-Wise General Studies MCQs
Enhance your analytical skills with Clocks MCQs. Practice standard UPSC-level time and angle problems with detailed explanations to improve accuracy in the CSAT examination.
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Explanation: Strategy: Use Angle = |30H - 5.5M|. At 12:20, hour hand = 0 + 0.5×20 = 10°, minute hand = 6×20 = 120°. The difference is 110°, which is the smaller angle.
Explanation: Strategy: The clock regains correct display when the total gain equals 12 hours (720 minutes). At 15 minutes gained per day, this requires 720 ÷ 15 = 48 days.
Explanation: Strategy: For hands to be opposite, the angle must be 180°. Using 30H - 5.5M = 180, substitute H = 9: 270 - 5.5M = 180, giving M = 90/5.5 = 180/11 = 16 4/11 minutes.
Explanation: Strategy: From 7:00 AM to 7:00 PM is 12 actual hours. The watch gains 5 minutes per hour, so total gain = 12 × 5 = 60 minutes = 1 hour. The watch will show 7:00 PM + 1 hour = 8:00 PM.
Explanation: Strategy: From 6:00 AM to 6:00 PM is 12 actual hours. The watch gains 2 minutes per hour, so total gain = 12 × 2 = 24 minutes. The watch will display 6:00 PM + 24 minutes = 6:24 PM.
Explanation: Strategy: Use 30H - 5.5M = ±60. Between 11 and 12, solving 30×11 - 5.5M = 60 gives 330 - 5.5M = 60, so 5.5M = 270, and M = 540/11 = 49 1/11 minutes. This is the only occurrence in this hour.
Explanation: Strategy: Use the mirror time formula: Actual Time = 11:60 - Mirror Time. For 5:25, subtract from 11:60 to get 6:35. Verify: 5:25 + 6:35 = 12:00.
Explanation: Strategy: Use 30H - 5.5M = ±120. Between 2 and 3, solving 30×2 - 5.5M = -120 gives 60 - 5.5M = -120, so 5.5M = 180, and M = 360/11 = 32 8/11 minutes. This is the only occurrence in this hour.
Explanation: Use the formula: Angle = |30H - 5.5M|. At 4:20, hour hand position = 30×4 + 0.5×20 = 130°, minute hand position = 6×20 = 120°. The difference is 10°. Since 10° < 180°, the angle is 10°.
Explanation: Strategy: Use the mirror time formula: Actual Time = 11:60 - Mirror Time. For 7:20, subtract from 11:60 to get 4:40. Verify: 7:20 + 4:40 = 12:00.
Explanation: Strategy: Use 30H - 5.5M = ±75. For the second occurrence between 4 and 5, solve 30×4 - 5.5M = -75, giving 120 - 5.5M = -75, so 5.5M = 195, and M = 390/11 = 35 5/11 minutes.
Explanation: Strategy: In 12 hours, the hands are at 90° exactly 22 times. They are perpendicular twice in each hour, except that the 2nd and 8th occurrences align with hour transitions in a way that still counts as distinct times within the 12-hour cycle.
Explanation: Strategy: Use 30H - 5.5M = ±100. For the first occurrence between 7 and 8, solve 30×7 - 5.5M = 100, giving 210 - 5.5M = 100, so M = 110/5.5 = 20 minutes. The time is 7:20.
Explanation: Strategy: For hands to coincide, use 30H - 5.5M = 0. Substituting H = 9 gives 270 = 5.5M, so M = 270/5.5 = 540/11 = 49 1/11 minutes.
Explanation: Strategy: Use Angle = |30H - 5.5M|. At 11:10, hour hand = 30×11 + 0.5×10 = 335°, minute hand = 6×10 = 60°. The difference is 275°, so the smaller angle is 360° - 275° = 85°.
Explanation: Strategy: Use Angle = |30H - 5.5M|. At 8:25, hour hand = 30×8 + 0.5×25 = 252.5°, minute hand = 6×25 = 150°. The difference is 102.5°, which is the smaller angle.
Explanation: Strategy: The clock shows correct time again when the total loss equals 12 hours (720 minutes). At 20 minutes lost per day, the required number of days = 720 ÷ 20 = 36 days.
Explanation: Strategy: Use the mirror time formula: Actual Time = 11:60 - Mirror Time. For 8:50, subtract from 11:60 to get 3:10. Verify: 8:50 + 3:10 = 12:00.
Explanation: Strategy: Use 30H - 5.5M = ±90. For the second perpendicular between 6 and 7, solve 30×6 - 5.5M = -90, giving 180 - 5.5M = -90, so 5.5M = 270, and M = 270/5.5 = 540/11 = 49 1/11 minutes.
Explanation: Strategy: The clock runs at 58 minutes per actual hour. From 8:00 AM to 10:00 AM on the clock is 2 clock-hours = 120 clock-minutes. Actual time elapsed = 120 × (60/58) = 3600/29 minutes ≈ 2 hours 4 minutes. The actual time is approximately 10:04 AM.
Explanation: Strategy: Use Angle = |30H - 5.5M|. At 3:40, hour hand = 30×3 + 0.5×40 = 110°, minute hand = 6×40 = 240°. The difference is 130°, which is the smaller angle.
Explanation: Strategy: The watch loses 1.5 minutes per hour, so it runs at 58.5/60 of actual speed. From 5:00 AM to 8:30 PM is 15.5 hours on the watch. Actual time elapsed = 15.5 × (60/58.5) = 15 hours 54 minutes approximately. Adding to 5:00 AM gives 8:54 PM.
Explanation: Strategy: For hands to be in a straight line but not overlapping, the angle must be 180°. Using 30H - 5.5M = 180, substitute H = 10: 300 - 5.5M = 180, giving M = 120/5.5 = 240/11 = 21 9/11 minutes.
Explanation: Strategy: The hands coincide once every 12/11 hours. In 12 hours, they coincide 11 times (not 12, because the 11th coincidence is just before 12:00). Therefore, in 24 hours, they coincide 22 times.
Explanation: Strategy: A clock shows the correct time again when the total accumulated error equals 12 hours (720 minutes). If it loses 8 minutes per day, the required number of days = 720 ÷ 8 = 90 days.
Explanation: Strategy: From 12:00 noon to 6:00 PM is 6 actual hours. The watch gains 10 minutes per hour, so total gain = 6 × 10 = 60 minutes = 1 hour. The watch will show 6:00 PM + 1 hour = 7:00 PM.
Explanation: Strategy: Use Angle = |30H - 5.5M|. At 7:35, hour hand = 30×7 + 0.5×35 = 227.5°, minute hand = 6×35 = 210°. The difference is 17.5°, which is the smaller angle.
Explanation: Strategy: The clock runs at 59 minutes per actual hour. From 7:00 AM to 1:00 PM on the clock is 6 clock-hours. Actual time elapsed = 6 × (60/59) = 360/59 hours ≈ 6 hours 6 minutes. The actual time is approximately 1:06 PM.
Explanation: Strategy: Calculate the actual time elapsed and apply the gain rate. From 8:00 AM to 4:00 PM is 8 actual hours. The clock gains 5 minutes per hour, so total gain = 8 × 5 = 40 minutes. The clock will show 4:00 PM + 40 minutes = 4:40 PM.
Explanation: Strategy: Recognize that the time depends on the intervals between strikes, not the strikes themselves. Striking 6 involves 5 intervals, so each interval = 1 second. Striking 12 involves 11 intervals, requiring 11 seconds.
Explanation: Strategy: The clock runs at 66 minutes per actual hour. From 10:00 AM to 4:00 PM on the clock is 6 clock-hours. Actual time elapsed = 6 × (60/66) = 60/11 hours ≈ 5 hours 27 minutes. The actual time is approximately 3:27 PM.
Explanation: Strategy: For hands to be opposite, the angle between them must be 180°. Using 30H - 5.5M = 180, substitute H = 8: 240 - 5.5M = 180, giving M = 60/5.5 = 120/11 = 10 10/11 minutes.
Explanation: Strategy: In 12 hours, the hands coincide 11 times and are opposite each other 11 times. Therefore, they are in a straight line 22 times in 12 hours.
Explanation: Strategy: Use Angle = |30H - 5.5M|. At 2:40, hour hand = 30×2 + 0.5×40 = 80°, minute hand = 6×40 = 240°. The difference is 160°. Since 160° < 180°, the angle is 160°.
Explanation: Strategy: The clock shows correct time again when the total gain equals 12 hours (720 minutes). At 20 minutes gained per day, the required number of days = 720 ÷ 20 = 36 days.
Explanation: Strategy: Use Angle = |30H - 5.5M|. At 9:45, hour hand = 30×9 + 0.5×45 = 292.5°, minute hand = 6×45 = 270°. The difference is 22.5°, which is less than 180°, so the smaller angle is 22.5°.
Explanation: Strategy: Use 30H - 5.5M = ±30. For the first occurrence between 5 and 6, solve 30×5 - 5.5M = 30, giving 150 - 5.5M = 30, so M = 120/5.5 = 240/11 = 21 9/11 minutes.
Explanation: Strategy: Use Angle = |30H - 5.5M|. At 5:15, hour hand = 30×5 + 0.5×15 = 157.5°, minute hand = 6×15 = 90°. The difference is 67.5°, which is the smaller angle.
Explanation: Use the formula: 30H - 5.5M = ±90. Between 3 and 4, solving 30×3 - 5.5M = -90 gives 5.5M = 180, so M = 360/11 = 32 8/11 minutes. The first right angle occurs at 3:00; the second occurs at 3:32 8/11.
Explanation: Strategy: In 12 hours, the hands coincide 11 times and are opposite each other 11 times, giving 22 straight-line positions. Therefore, in 24 hours, this occurs 44 times.
Explanation: Strategy: Use 30H - 5.5M = ±50. For the first occurrence between 3 and 4, solve 30×3 - 5.5M = 50, giving 90 - 5.5M = 50, so M = 40/5.5 = 80/11 = 7 3/11 minutes.
Explanation: Strategy: Use the mirror time formula: Actual Time = 11:60 - Mirror Time. For 3:15, subtract from 11:60 to get 8:45. Alternatively, actual time + mirror time = 12:00.
Explanation: Strategy: The watch runs at 52 minutes per actual hour. From 4:00 PM to 10:00 PM on the watch is 6 watch-hours. Actual time elapsed = 6 × (60/52) = 90/13 hours ≈ 6 hours 55 minutes. The actual time is approximately 10:55 PM.
Explanation: Strategy: From 11:00 PM to 5:00 AM is 6 actual hours. The clock gains 8 minutes per hour, so total gain = 6 × 8 = 48 minutes. The clock will show 5:00 AM + 48 minutes = 5:48 AM.
Explanation: Strategy: The clock runs at 54 minutes per actual hour. From 12:00 noon to 3:00 PM on the clock is 3 clock-hours = 180 clock-minutes. Actual time elapsed = 180 × (60/54) = 200 minutes = 3 hours 20 minutes. The actual time is 3:20 PM.
Explanation: Strategy: The clock shows correct time again when the total loss equals 12 hours (720 minutes). At 15 minutes lost per day, the required number of days = 720 ÷ 15 = 48 days.
Explanation: Strategy: From 6:00 AM to 2:00 PM is 8 actual hours. The clock loses 5 minutes per hour, so total loss = 8 × 5 = 40 minutes. The clock will show 2:00 PM - 40 minutes = 1:20 PM.
Explanation: Strategy: From 9:00 PM to 6:00 AM is 9 actual hours. The clock gains 3 minutes per hour, so total gain = 9 × 3 = 27 minutes. The clock will show 6:00 AM + 27 minutes = 6:27 AM.
Explanation: Strategy: Use 30H - 5.5M = ±130. For the first occurrence between 6 and 7, solve 30×6 - 5.5M = 130, giving 180 - 5.5M = 130, so M = 50/5.5 = 100/11 = 9 1/11 minutes.
Explanation: Strategy: From 9:00 AM to 3:00 PM is 6 actual hours. The clock loses 3 minutes per hour, so total loss = 6 × 3 = 18 minutes. The clock will show 3:00 PM - 18 minutes = 2:42 PM.
Explanation: Strategy: For hands to coincide, the angle between them is 0°. Using 30H - 5.5M = 0, substitute H = 5: 150 = 5.5M, giving M = 150/5.5 = 300/11 = 27 3/11 minutes.
Explanation: Strategy: The clock shows correct time again when it has gained exactly 12 hours (720 minutes). At 4 minutes per hour, this requires 720 ÷ 4 = 180 hours = 7.5 days. Starting from Monday noon, adding 7.5 days reaches Monday midnight.
Explanation: Strategy: Use the mirror time formula: Actual Time = 11:60 - Mirror Time. For 10:40, subtract from 11:60 to get 1:20. Verify: 10:40 + 1:20 = 12:00.
Explanation: Strategy: Use 30H - 5.5M = ±90. Between 1 and 2, solving 30×1 - 5.5M = -90 gives 5.5M = 120, so M = 240/11 = 21 9/11 minutes. This is the only perpendicular occurrence in this hour.
Explanation: Strategy: The clock shows correct time again when the total error equals 12 hours (720 minutes). At 10 minutes lost per day, the required number of days = 720 ÷ 10 = 72 days.
Explanation: Strategy: The time depends on intervals between strikes, not the strikes themselves. Striking 4 involves 3 intervals, so each interval = 2 seconds. Striking 8 involves 7 intervals, requiring 14 seconds.
Explanation: Strategy: For coincidence, use 30H - 5.5M = 0. Substituting H = 1 gives 30 = 5.5M, so M = 30/5.5 = 60/11 = 5 5/11 minutes.
Explanation: Strategy: The watch runs at 56 minutes per actual hour. From 8:00 AM to 2:00 PM on the watch is 6 watch-hours. Actual time elapsed = 6 × (60/56) = 45/7 hours ≈ 6 hours 26 minutes. The actual time is approximately 2:26 PM.
Explanation: Strategy: Use 30H - 5.5M = ±90. Between 12 and 1, solving 30×12 - 5.5M = 90 gives 360 - 5.5M = 90, so 5.5M = 270, and M = 540/11 = 49 1/11 minutes. This is the only perpendicular occurrence in this hour.
Explanation: Strategy: The clock shows correct time again when the total gain equals 12 hours (720 minutes). At 12 minutes gained per day, the required number of days = 720 ÷ 12 = 60 days.