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Clocks and calendars Concept for the CAT exam

CAT stands for common aptitude test. This topic is an integral part of many competitive exams. An aspirants could except few questions from this Clocks and calendars topic. As Logical reasoning section contain a total of 20 questions and out of that few questions are from Clocks and calendars . A Logical Reasoning & Data Interpretation contains 30% weightage in CAT exams.

Clocks and calendars- Basic Concepts

Questions on clocks (or even calendars) are not really frequent in CAT these days. They used to be really popular few years ago. Having said that, it is always better to understand some of the basic principles and the types of problems that get asked. They might come in handy in case of other exams like CMAT, MAT, SNAP, etc.

Clock problems can be broadly classified in two categories:

  • Problems on angles
  • Problems on incorrect clocks

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Important Formula’s of Clocks and calendars

Clocks Important Formulas

Few formula’s that you should know to solve questions related to clocks are as follow:

  1. 60-minute space = 360° = 1 hour
  2. 1-minute space = 6° = 1 minute
  3. 5-minute space = 6° x 5 = 30° = 5 minutes
  4. Right Angle or Perpendicular = 15-minute spaces apart
  5. Right Angle or Perpendicular = 22 times in 12 hours or 44 times in 24 hours (1 day)
  6. Speed of minute hand = 6 dpm
  7. Straight Angle or Straight Line or 180° = 30-minute space apart
  8. Straight Angle = 11 times in 12 hours or 22 times in 24 hours (1 day)
  9. Angle traced by hour hand in 12 hrs = 360°
  10. Angle traced by minute hand in 60 min. = 360°
  11. Speed of hour hand = 0.5 dpm (degree per minute)
  12. Angle of the hour hand from vertical at N o’clock = 30N

Calendar Important Formula’s

Few formula’s that you should know to solve questions related to calendars are as follow:

  1. 1 ordinary year = 365 days = (52 weeks + 1 day.)
  2. 1 ordinary year has 1 odd day. 1 leap year has 2 odd days. = (76 x 1 + 24 x 2) odd days = 124 odd days.

Remember the Number of days in a Months for calendar.

While it may sound as an insignificant preparation tip, it is crucial that the candidate knows the months having 30 days and the ones having 31 days, as the number of days in a month is an essential part of solving questions on calenders.

Months having 30 days in a month.

  1. April
  2. June
  3. September
  4. November

Months having 31 days in a month.

  1. January
  2. March
  3. May
  4. July
  5. August
  6. October
  7. December

Special Month : February

  • Depending on whether the year is a leap year or not.
  • Leap years are exactly divisible by 4
  • February can have : 28 Days or 29 Days (For Leap Year)

Video’s that could help aspirant.

Problems on angles of Clocks

Before we actually start solving problems on angles, we need to get couple of basic facts clear:

  • Speed of the hour hand = 0.5 degrees per minute (dpm) {The hour hand completes a full circle or 360 degrees in 12 hours or 720 minutes}
  • Speed of the minute hand = 6 dpm {The minute hand completes a full circle in 60 minutes}
  • At ‘n’ o’ clock, the angle of the hour hand from the vertical is 30n

For Example 1: What is the angle between the hands of the clock at 7:20

At 7 o’ clock, the hour hand is at 210 degrees from the vertical.

In 20 minutes, Hour hand = 210 + 20*(0.5) = 210 + 10 = 220 {The hour hand moves at 0.5 dpm}

Minute hand = 20*(6) = 120 {The minute hand moves at 6 dpm}. Difference or angle between the hands = 220 – 120 = 100 degrees

Problems on incorrect clocks

Such sort of problems arise when a clock runs faster or slower than expected pace. When solving these problems it is best to keep track of the correct clock.

For Example 2: A watch gains 5 seconds in 3 minutes and was set right at 8 AM. What time will it show at 10 PM on the same day?

Ans: The watch gains 5 seconds in 3 minutes => 100 seconds in 1 hour. From 8 AM to 10 PM on the same day, time passed is 14 hours. In 14 hours, the watch would have gained 1400 seconds or 23 minutes 20 seconds. So, when the correct time is 10 PM, the watch would show 10 : 23 : 20 PM

CAT Clock and Calendars Solved Question

For example 1. What is the angle between the two hands of a clock when the time shown by the clock is 6.30 p.m. ?

a) 60
b) 50
c)30
d)150

Answer: option d
Explanation: q = 11/2 m – 30h
= 11/2 *30 – 30 *6
= /165-180/ = 150

For example 2. At what time between 3 and 4 o’clock will the minute hand and the hour hand are on the same straight line but facing opposite directions.

a) 3:49
b)3:15
c)3:39 1/11
d)3:49 1/11

Answer: option d
Explanation : On straight line means 180 degree angle.
180 = 11/2m- 30h
then, 180 = 11/2 m –30*3
180 = 11/2m-90
(180+90)2 = 11m
m = 540/11 = 49 1/11

For Example 3. By how many degrees does the minute hand move in the same time, in which the hour hand move by 280 ?

a)168
b)336
c) 196
d) 376

Answer: option b
Explanation: 28*2 *6 = 3360

Practice questions of Clock and Calendars

Question 1. Find out the angle between the hands of the clock at 7:20?

  1. 100 degree
  2. 200 degree
  3. 300 degree
  4. 400 degree

Correct Answer: (A)

Question 2. Calculate the time the hands of the clock meet between 7:00 and 8:00?

  1. 7 : 38 : 2/11th
  2. 8 : 38 : 2/11th
  3. 6 : 38 : 2/11th
  4. 3 : 38 : 2/11th

Correct Answer: (A)

Question 3. Find out the time the hands of a clock between 7:00 and 8:00 form 90 degrees?

  1. 8 : 21 : 9/11th and 7 : 54 : 6/11th
  2. 7 : 21 : 9/11th and 7 : 54 : 6/11th
  3. 9 : 21 : 9/11th and 7 : 54 : 6/11th
  4. 6 : 21 : 9/11th and 7 : 54 : 6/11th

Correct Answer: (B)

Question 4. A clock gains 5 seconds in 3 minutes. It was set right at 8 AM. Calculate the time that it will show at 10 PM on the same day?

  1. 9 : 23 : 20 PM
  2. 10 : 23 : 20 PM
  3. 8 : 23 : 20 PM
  4. 7 : 23 : 20 PM

Correct Answer: (B)

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