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

There are two clocks, A and B. Clock A is a regular clock, while Clock B is defective. Clock B gains 20 minutes every hour. Both clocks are set to 12:00 p.m. Find the time in Clock B when Clock A shows 3:24 p.m.

  1. 4:24 p.m.

  2. 3:04 p.m.

  3. 4:32 p.m.

  4. 3:42 p.m.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Clock A shows 3 hours 24 minutes (204 minutes). Clock B gains 20 minutes per hour, meaning it runs at 80 minutes per actual hour (or 4/3 speed). In 204 minutes, Clock B will show 204 * (4/3) = 272 minutes. 272 minutes = 4 hours 32 minutes. Time is 4:32 p.m.

Multiple choice

Find the angle between the hour and minute hands of a clock at 5:55 p.m.

  1. 150°

  2. 152.5°

  3. 155.5°

  4. 125.5°
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

At 5:55, the minute hand is at 11 (55 minutes). The hour hand is at 5 + 55/60 = 5 + 11/12 = 71/12. The angle of the minute hand from 12 is 55 * 6 = 330 degrees. The angle of the hour hand from 12 is (71/12) * 30 = 177.5 degrees. The difference is |330 - 177.5| = 152.5 degrees.

Multiple choice

At what time between 2 PM and 3 PM will the hour and minute hands of a clock be exactly opposite each other?

  1. 2:16:21

  2. 2:27:16

  3. 2:43:38

  4. 2:49:45
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

At 2 PM, the minute hand is at 12 and the hour hand is at 2. For the hands to be opposite, the minute hand must be 30 minutes ahead of the hour hand, meaning it must be at the 8 o'clock position (40 minutes). Using the formula M = (2/11) * (30 * H + 30), where H=2, we get M = (2/11) * 90 = 180/11 = 16.36 minutes, which corresponds to 2:43:38 when calculating the exact position for the hands to be 180 degrees apart.

Multiple choice

A clock was set correctly at 12:00 noon. It gains 10 minutes every hour. Later, the same clock shows 3:00 PM. What is the correct actual time then?

  1. 2:48:00 PM

  2. 2:34:17 PM

  3. 2:45:00 PM

  4. 2:50:00 PM
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The clock gains 10 minutes every hour, meaning it shows 70 minutes for every 60 minutes of real time. Ratio = 7/6. The clock shows 3 hours passed (12:00 to 3:00). Actual time passed = 3 * (6/7) = 18/7 hours = 2 hours and 34.28 minutes. 2 hours 34 minutes and 17 seconds.

Multiple choice

It is between 3 pm and 4 pm and the distance between the hour hand and the minute hand of clock is 18 minutes spaces. What time does the clock show ?

  1. 3 : 12 pm

  2. 3 : 27 pm

  3. 3 : 31 pm

  4. 3 : 36 pm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

At 3:x, the hour hand is at 15 + x/12 minute marks. The minute hand is at x. The difference is |x - (15 + x/12)| = 18. Case 1: x - 15 - x/12 = 18 => 11x/12 = 33 => x = 36. Case 2: 15 + x/12 - x = 18 => -11x/12 = 3 => x is negative (invalid). So 3:36 pm.

Multiple choice

At what time between 5 and 6 will the hands of a clock coincide.

  1. 200/11

  2. 300/11

  3. 400/11

  4. 250/11
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

At 5 o'clock, the minute hand is 25 minutes behind the hour hand. To coincide, the minute hand must gain 25 minutes. The gain rate is 55/60 minutes per minute. Time = 25 / (55/60) = 1500/55 = 300/11 minutes past 5.