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

Akash went out between 7 o'clock and 8 o'clock. At 8:30 pm, he realised that the minute hand of the clock was as much behind the hour hand as the hour hand was behind the minute hand when he had gone out. At what time did Akash go out?

  1. 519/11 minutes past 7 o'clock

  2. 359/11 minutes past 7 o'clock

  3. 309/11 minutes past 7 o'clock

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let Akash go out at 7:x. Hour hand position = 30*7 + 0.5x. Minute hand = 6x. At 8:30, hour hand = 30*8 + 0.5*30 = 255 degrees. Minute hand = 180 degrees. The problem states the relative positions are swapped. Solving the linear equations leads to 51 9/11 minutes past 7.

Multiple choice

The minute hand of a clock crosses the hour hand x minutes past 7 in the evening. Some guests come 20 minutes later. At what time do the guests come?

  1. 7:58:11 pm

  2. 7:10:27 pm

  3. 7:45:15 pm

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

At 7:00, the minute hand is 35 minute spaces behind the hour hand. Since the minute hand gains 55 minute spaces over the hour hand every 60 minutes, it will overtake the hour hand at 35 * (60/55) = 38 and 2/11 minutes past 7. Adding 20 minutes to this gives 58 and 2/11 minutes past 7, which is approximately 7:58:11 pm.

Multiple choice

Sanju has two watches with a 12-hour cycle. One of these watches gains one minute a day and the other loses 1 and 1/2 minutes per day. If Sanju sets both the watches at the correct time, how long will it be before they again show the correct time together?

  1. 482 days

  2. 290 days

  3. 1440 days

  4. 730 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Relative gain = 1 - (-1.5) = 2.5 minutes per day. To show the correct time again, the watch must gain or lose a full 12-hour cycle (720 minutes). Days = 720 / 0.5 = 1440 (since the watches are 12-hour cycles, we need to gain 720 minutes).

Multiple choice

It is between 9 and 10 o'clock that a boy looking at his watch mistakes the hour-hand for the minute-hand and thinks that the time of the day is 53 minutes earlier than the real time. What is the exact time?

  1. 40 ½ min. past 9

  2. 415/11 min. past 9

  3. 40 ½ min. past 8

  4. 45 5/11 min. past 9

  5. 20 min. past 8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the time be 9:x. The hour hand is at 9 + x/60, minute hand at x. The mistake swaps them. The difference between the actual time and the perceived time is 53 minutes. Solving the equation leads to 41 5/11 minutes past 9.

Multiple choice

Munish's watch loses 6 minutes per day. On Monday morning at 11 o'clock, it is 45 minutes ahead of the actual time. If Atul sets his watch according to Munish's watch on Friday evening at 5 o'clock, then Atul's watch will be

  1. 19.5 min behind the time

  2. 25 min ahead of the actual time

  3. 19.5 min ahead of actual time

  4. correct
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Munish's watch loses 6 min/day. From Monday 11 AM to Friday 5 PM is 4 days + 6 hours = 102 hours. Total loss = (6/24) * 102 = 25.5 minutes. It was 45 min ahead, so it is now 45 - 25.5 = 19.5 min ahead of actual time.

Multiple choice

A watch which gained 5 seconds in 3 minutes, was set right at 7 a.m. In the afternoon on the same day, when the watch indicated quarter past 4 o'clock, the actual time was

  1. 5 p.m.

  2. 4 p.m.

  3. 3 p.m.

  4. 2 p.m.
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 * 20 = 100 seconds. From 7 a.m. to 4:15 p.m. is 9 hours and 15 minutes (555 minutes). Total gain = (555/3) * 5 = 185 * 5 = 925 seconds = 15 minutes and 25 seconds. If the watch shows 4:15, the actual time is 4:15 minus 15m 25s, which is approximately 4 p.m.

Multiple choice

Arjun goes out at some time between 2 o'clock and 3 o'clock and returns between 4 o'clock and 5 o'clock. He notices that the hands of the clock have exactly interchanged their positions. At what time did he go out?

  1. 15 140 143 past 2 o'clock

  2. 20 70 143 past 2 o'clock

  3. 20 140 143 past 2 o'clock

  4. 30 140 143 past 2 o'clock

  5. 40 140 143 past 2 o'clock
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When hands interchange, the time is given by T = 60/143 * (5H + M) minutes past H. For 2 to 3 o'clock, H=2. The formula for interchanged hands is 60/143 * (5H2 + M2) = M1 and 60/143 * (5H1 + M1) = M2. Solving this results in 20 140/143 minutes past 2.

Multiple choice

What is the angle between the hour hand and minute hand of a clock at 5:35 PM?

  1. 42 ½0

  2. 46 ½0

  3. 48 ½0

  4. 50 ½0
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

At 5:35 PM, the minute hand is at 7 (which corresponds to 210 degrees from 12 o'clock). The hour hand has moved past 5 by 35/60 of the space between 5 and 6, so its position is 5 * 30 + (35/60) * 30 = 150 + 17.5 = 167.5 degrees. The absolute difference between their positions is 210 - 167.5 = 42.5 degrees, which is written as 42 1/2 degrees (garbled in text as 42 ½0).

Multiple choice

For a project, a few computer science students form a virtual planet called SRAM. They introduce a new calendar and time period structure where there are 8 days per week, starting Sunday to Saturday and another day called Funday. Every day is of 36 hours and each hour is of 90 minutes. Each minute is of 60 seconds. Hour hand covers the dial twice daily. What is the angle between the hour and minute hand when time is 12.18 am?

  1. 120°

  2. 135°

  3. 152°

  4. 172°

  5. 164°
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

There are clocks A and B. The hands of clock A move normally as clockwise, while in clock B (due to reverse connection), they move anticlockwise. Initially, the two hands of both clocks are at mark showing 12. If after some time, the angle between the directions of two hour hands is 90° (for the first time), then at the same instant, the angle between the directions of minute hand will be

  1. 0°

  2. 15°

  3. 30°

  4. 45°

  5. 60°
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The hour hand of clock A moves clockwise at 0.5 degrees per minute, and the hour hand of clock B moves anticlockwise at 0.5 degrees per minute. If they start at 12, their positions at time t are 0.5t and -0.5t. The angle between them is |0.5t - (-0.5t)| = |t| = 90 degrees. At t = 90 minutes, the minute hand of A is at 90 * 6 = 540 degrees (mod 360) = 180 degrees, and the minute hand of B is at -540 degrees (mod 360) = 180 degrees. Thus, the angle between them is 0 degrees.