Quantitative Aptitude

Clocks and Calendars

428 Questions
All Angle between hands 150 Clock gaining or losing time 132 Clock hands coincidence 69 Right angle times 30 Find time from angle 21 Decoding mixed date formats 7 Find day using reference date 6 Repeating same calendar 6 Date without reference day 3

Clocks and Calendars Questions

Multiple choice

I purchased some clocks from a second hand goods store. There were some problems in them. When the actual time passed 1 hour, the wall clock was 10 minutes behind it. When 1 hour was shown by the wall clock, the table clock showed 10 minutes ahead of it. When table clock showed 1 hour, the alarm clock was 5 minutes behind it. When alarm clock showed 1 hour, the wrist watch was 5 minutes ahead of it. Assuming that all clocks are correct with actual time at 12 noon, what will be shown by the wrist watch after 6 hours?

  1. 4:38 pm

  2. 5:15 pm

  3. 5:36 pm

  4. 5:47 pm

  5. 6:47 pm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Wall clock: 1h actual = 50m wall. Table clock: 1h wall = 70m table. Alarm clock: 1h table = 55m alarm. Wrist watch: 1h alarm = 65m wrist. After 6 hours actual time: Wall = 6 * 50 = 300m. Table = 300 * (70/60) = 350m. Alarm = 350 * (55/60) = 320.83m. Wrist = 320.83 * (65/60) = 347.5m = 5h 47.5m. 12:00 + 5h 47.5m = 5:47 pm.

Multiple choice

A watch was set right at 7 am. It gains 5 seconds in 3 minutes. In the afternoon of the same day, when the watch indicated 4:15, the true time was

  1. 3:55 pm

  2. 4:00 pm

  3. 4:05 pm

  4. 4:10 pm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The watch gains 5 seconds every 3 minutes. In 1 hour (60 minutes), it gains (5/3) * 60 = 100 seconds. From 7 am to 4:15 pm is 9 hours and 15 minutes = 555 minutes. Total gain = (5/3) * 555 = 925 seconds = 15 minutes and 25 seconds. If the watch shows 4:15, the true time is 4:15 - 15m 25s = 3:59:35 pm, which is approximately 4:00 pm.

Multiple choice

If the hour-hand and the minute-hand of a clock coincide every 64 minutes, how much does the clock gain or lose everyday?

  1. 60 min

  2. 35 min

  3. 33 8 11 m i n

  4. 32 8 11 m i n

  5. 62 8 11 m i n
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The hands of a clock coincide every 65 and 5/11 minutes. If they coincide every 64 minutes, the clock is gaining time. The gain per 64 minutes is (65 and 5/11 - 64) = 1 and 5/11 = 16/11 minutes. Daily gain = (16/11) * (24 * 60 / 64) = 32 and 8/11 minutes.

Multiple choice

At what time between 4 o'clock and 5 o'clock will the hands of a clock point in opposite directions?

  1. 56 5 11 minutes past 4

  2. 54 6 11 minutes past 4

  3. 52 9 11 minutes past 4

  4. 57 3 11 minutes past 4

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

At 4 o'clock, the hour hand is 120 degrees ahead of the minute hand. For the hands to point in opposite directions, the minute hand must gain 120 + 180 = 300 degrees relative to the hour hand. Since the relative speed of the minute hand is 5.5 degrees per minute, the time required is 300 / 5.5 = 54 6/11 minutes past 4.

Multiple choice

At what time between 10 o'clock and 11 o'clock are the two hands of a clock symmetric with respect to the vertical line (give the answer to the nearest second)?

  1. 10h 9m 13s

  2. 10h 9m 14s

  3. 10h 9m 22s

  4. 10h 9m 50s
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Symmetry with respect to the vertical line (the 12-6 axis) means the sum of the angles of the hands from the 12 o'clock position must be 360 degrees. At 10:x, the hour hand is at 300 + 0.5x degrees and the minute hand is at 6x degrees. Solving 300 + 0.5x + 6x = 360 gives 6.5x = 60, so x = 120/13 minutes, which is approximately 9 minutes and 13.8 seconds.