Calendar, Clocks, Train related questions

Introduction

Questions on calendar clocks and trains are given to check one’s aptitude. They can be solved by simple formulae and quick maths. We just have to know how each system of calendar, clocks and train works and we will be easily able to identify what day it is, the time it is or the speed of the train.

Arithmetic

Arithmetic is a branch of maths that helps us study numbers with the help of various operations such as addition (+), subtraction (-), multiplication (*), division (/).

For example, in 3, 6, 9, 12,.. the difference will always be 3. Such an ordered list of numbers is called a sequence and each number is regarded as a term. Sequences have a pattern, which helps us identify what number is going to come next. In 25,20,15,10.. we have to subtract 5 from each term to get the next term. Sequences with specific patterns are called arithmetic sequences.

Calendar, Clocks, Train related questions

The year consists of 365 days and 366 in leap year once every 4 years. To find the day of the given problem, we need to remember the following-

i) If the 1st of January was a Monday, we count the days from Sunday. So the 0th day is Sunday and also the 7th will be Sunday.

ii) Each day gets repeated after 7 days. So if the 14th is the Monday, the next Monday will be the next multiple of Monday. So if a month has 30 days, it will be calculated by 30/7, which comes out to be 4 weeks and 2 days. These two days are called the odd days.

iii) In a normal year there are 365 days which comes to 52 weeks and with 1 odd day but in a leap year there are 366 days so, we’ll have 52 weeks and with 2 odd days.

iv) In 100 years, there are 76 years and 24 leap years, so the number of odd days is 124, which comes out to be 17 weeks and 5 days. So, in 100 years we have 5 odd days.

v) 400 and all the multiples of 400 are leap years.

The formulas for solving train problems are-

i) Speed of the train = Distance/Time

ii) Speed = Total distance covered by the train/Time taken

iii) To convert kilometre/hour to meters/second we have to multiply it with 5/18

iv) To convert meters/second to kilometre/hour, we have to multiply it by 18/5

Clock question

If the clock shows 6:15 and the actual time is 6, then the clock is said to be 15 minutes fast. While the clock indicates 5:45 and the actual time is 6, then the clock is said to be 15 minutes slow. Some formulas for the clock are-

1. 60-minute = 360° = 1 hour
2. 1-minute = 6° = 1 minute
3. 5-minute = 6° x 5 = 30° = 5 minutes
4. Right Angle = 15-minute spaces apart
5. Right Angle = 22 times in 12 hours or 44 times in 24 hours
6. Straight Angle or Straight Line = 30-minute space apart
7. Straight Angle = 11 times for 12 hours or 22 times for 24 hours
8. Angle covered by hour hand in 12 hrs = 360°
9. Angle covered by minute hand in 60 min. = 360°
10. Speed of hour hand = 0.5 degrees per minute
11. Speed of minute hand = 6 degrees per minute

Clock reasoning questions

There are multiple types of clock reasoning questions, they are-

i) Angle based clock

ii) Reflection of clock

iii) Defective clock

Clocks aptitude

There are particular points to remember while solving clock aptitude questions,  they are-

i) A clock 9 is divided into 60 equal parts. These 60 equal parts are called minutes.

ii) A clock has two hands, one is the hour hand and one is the minute hand. The hour hand is smaller than the minute hand.

iii) In one hour, the hour hand moves one number ahead and the minute hand finishes a full circle of the clock. Thus in one hour, the minute hand gains 55-minute spaces on the hour hand.

iv) The speed of the hour hand is 0.5 per minute as the hour hand goes around the clock in twelve hours. The angle covered by the hour hand is 360 degrees.

v) The minute hand goes around the clock in one hour and the total angle is 360 degrees. So, the speed of the minute hand is 6 degrees per minute.

vi) The hour and minute will coincide after every 65

Conclusion

We have learned all the formulae relating to clocks, calendars, and trains. They are simple problems given to checks one’s aptitude. One might think after reading the problems that there might be huge calculations but that is not the case. With simple formulas and with logical thinking, they are simple problems.