Quantitative Aptitude is an important section in terms of employment-related competitive exams all over India. This section is one of the key sections in recruitment exams all over India including but not limited to Railways, Banking, and Staff Selection Commission, Insurance, Teaching, UPSC and many others. This section has questions related to Percentage and Discount, Profit and Loss, Time and Work and  Clocks and Calendars etc.

Clock

Clocks – Important Terms:

Hour hand and minute hand

The smaller hand of a clock, which rotates around the clock once in every 12 hours is called the hour hand or shorthand and the larger hand ( instead of one ), which rotates around the clock once in every hour is called minute hand or long hand.

Minute Space

The complete circumference of the face or dial of the clock is divided into 60 equal parts called minute space.

Minute Gain

In every 60 minutes, the minute hand gains 55 minutes on the hour on the hour hand called the minute gain 

Overlap

In each hour, both the hands coincide only once. That coincidence is called an overlap.

Straight Line

The minute and hour hands are in the same straight line when they are coincident or opposite to each other forming a straight line.

Clock Too Fast

When a watch or a clock indicates 8.15, but the correct time is 8, the clock is said to be 15 minutes too fast.

Clock Too Slow

When a clock indicates 8:45, but the correct time is 8, the clock is said to be 15 minutes too slow.

Things to keep in mind

1. 60 minute space = 360° = 1 hour ( minute hand)
2. 1 minute space = 6° = 1 minute ( minute hand)
3. 5 minute space = 6° x 5 = 30° = 5 minutes (minute hand)
4. Right Angle or Perpendicular formed between the hour and minute hand = 15 minute spaces apart 
5. Right Angle or Perpendicular formed between the hour and minute hand = 22 times in 12 hours or 44 times in 1 day.
6. Straight Angle or Straight Line or 180°formed between the hour and minute hand  = 30-minute space apart
7. Straight Angle formed between the hour and minute hand = 11 times in 12 hours or 22 times in 1 day
8. Angle traced by the hour hand in 12 hrs = 360°
9. Angle traced by the minute hand in 60 min. = 360°
10. Speed of hour hand = ½ or 0.5 degree per minute
11. Speed of the minute hand = 6 degree per minute
12. Angle of the hour hand from vertical at N o’clock = 30 degrees.

Concepts & Types:

There are various types of questions under the clock.

Type 1: Find the time when the angle between the two hands is known.

Type 2: Find the angle between the 2 hands at known time.

Type 3: Questions on clocks when the clock is gaining or losing time.

Concept

1. The hand clock is a complete circle with a rotation of 360 degrees. The clock is divided into 12 equal parts and each part is 360/12 = 30°. 
2. When the minute hand takes a complete round in one hour, it covers 360° in 60 

minutes.

3. In 1 minute, the minute hand covers 360/60 = 6°/minute. 
4. The hour hand covers just one part out of the given 12 parts in one hour. 

This implies it covers 30° in 60 minutes i.e. ½° per minute.

5. This means that the relative speed of the minute hand is 6 – ½ = 5 ½ degrees. 
6. Also, we will be using the concept of relative speed and relative distance for solving problems related to clocks.

Tips:

• Tip 1: It would be easy to calculate the angle between the minute and the hour hand by using the formula given below,

Angle = (X*30) -((Y*11)/2)

• Tip 2: You can use this short formula for calculating the time when the angle is known

Angle = (minutes) -30 (hours)

Examples on

Example 1:

What would be the mirror image of the clock when the time is 01:40 

Solution→ 

We need to subtract the time ahead of 12:00 from 12:00 to get mirror image time Mirror image of 01:40 

Hence,

11:60 – 01:40 = 10:20

The mirror image of 1:40 would be 10:20.

Example 2:

When Rena looked at a clock,it was showing 6:00 in the morning. By how much angle will the hour’s hand rotate when she again looks at the clock at 12:00 in the noon?

Solution→ 

In 12 hours, the hour’s hand turns 360°

Hence, the difference between time = 6 hours

Therefore, the required angle = 360/12x 6 = 180°

Calendar

Calendars – Important Terms:

Ordinary year

The year which is not a special one that means the leap year is called an ordinary year. An ordinary year consists of 365 days.

Leap Year

A leap year has 366 days. It has an extra day i.e.29th day in the month of February.

Every year which is divisible by 4 is a leap year, if it is not a century. Every 4th year is a leap year and no other year could be a leap year.

Odd days

When we are supposed to find the day of the week on a given date, we use the concept of ‘odd days’. In a given time, the number of days more than the complete weeks are called odd days.

Things to keep in mind.

1.  A leap year consists of 366 days.
2. Every year which is divisible by 4 is a leap year, if it is not a century.
3. Every 4th century is a leap year and no other century other than the 4th one is a leap year.

Counting odd days

1. 1 ordinary year = 365 days = (52 weeks + 1 day)
2. Number of odd days in an ordinary year= 1.
3. 1 leap year = 366 days = (52 weeks + 2 days)
4. Number of odd days in the leap year= 2.
5. 100 years = (76 ordinary years + 24 leap years)

⇒  (76 x 1 + 24 x 2) odd days 

⇒ 124 odd days. 

⇒ (17 weeks + 5 days) 

⇒  5 odd days. 

Therefore the number of odd days in 100 years = 5.

1. Number of odd days in 200 years = (5 x 2) = 10 = 3 odd days

Tricks:

•  100 years has 5 odd days.
•  200 years has 5 x 2 = 10 – 7 (one week) = 3 odd days.
•  300 years has 5 x 3 = 15 – 14 (two weeks) = 1 odd day.
•  400 years has {5 x 4 + 1 (leap century)} – 21} (three weeks) = 0 odd days.
•  Month of January has 31 – 28 = 3 odd days. Same for the months of March, May, July, August, October and December.
• Month of February has 28 – 28 = 0 odd days in an ordinary year.
• Month of February has 1 odd day in a leap year.
• Month of March has 30-28 = 2 odd days. Same for April, June, September and November.

Important Note:

When you start counting from the beginning, that means for 1st January, 0001,

1. 1 odd day mean Monday is the odd day
2. 2 odd days mean Tuesday is the odd day
3. 3 odd days mean Wednesday and so on till 6 odd days which means Saturday.

Examples

Example 1:

If today is Monday. After 57 days, it would be:

Solution→ 

It is well known that each day of the week is repeated after 7 days. So, after 57 days, it will be a Monday again.

Example 2 

What was the week day on 17th June, 1998?

Solution→ 

17th June, 1998 = (1997 years + Period from 1/1/1998 to 17/6/1998)

Odd days in 1600 years = 0 odd day

Odd days in 300 years = 1 odd day

97 years has 24 leap years + 73 ordinary years.

Number of odd days in 97 years (24 x 2 + 73) = 121 = 2 odd days.

Jan, Feb, March, April, May, and June

(31 + 28 + 31 + 30 + 31 + 17) = 168 days

168 days = 24 weeks = 0 odd day.

Total number of odd days = (0 + 1 + 2 + 0) = 3 odd days.

It was Wednesday on 17th June, 1998.

Conclusion

Questions related to clock and time could be easily solved now. We have discussed every formula and tip to master this topic. You just need to practice more and more for investing least time on clock and calendar questions in your exam.