# Clocks and Calendars Concepts and Questions

## Calendar

A calendar is a specific measure of time. The smallest unit of calendar is a day. A day is an average time in which the earth completes one round on its axis. The time in which the earth travels around the sun is known a solar year.

#### One must remember the following points pertaining to a calendar:

(i) A solar year has 365 days 5 hours 48 minutes and 48 seconds. An ordinary year has 365 days. In order to remove this difference, every fourth year has 366 days and every fourth century is a leap year but no other century is a leap year.

(ii) The number of days more than the complete number of weeks in a given period is the number of odd days for that period.

(iii) In an ordinary year there are 52 weeks and one odd day.
• In a leap year there are 52 weeks and two odd days.
• 100 years contain 5 odd days.
• 200 years contain 3 odd days.
• 300 years contain 1 odd day.
• 400 years contain 0 odd days.
(iv) 1st January 1 A.D. was Monday. So days are counted according to this.: Sunday for 0 odd days: Monday for 1 odd day; Tuesday for 2 odd days, and so on.

## Clock

A clock or a watch is an instrument which shows time at a moment. The following points must be noted:

(i) The face or dial of a watch or a clock is a circle which is divided into 60 equal parts.It is called minute spaces
(ii) A clock or a watch has two hands, the smaller one is called hour hand the larger one is called minute hand
(iii) The hours are denoted from 1 to 12 and the minutes are indicated by marking from 1 to 60.
(iv) In one hour the minute hand passes over 60 minute spaces while the hour hand passes over 5 minute spaces. That is, in 60 minutes the minute hand gains 55 minute spaces (= 330°) on the hour hand.
(v) In every hour ––
(a) The hands coincide once,
(b) They point in opposite directions once and in this position, they are 30-minute spaces apart.
(c) They are twice at right angles and in these positions, they are 15 minute spaces apart

## Solved Questions from Previous Papers

### Question. 1

The angle bounded by the hands of a clock at 3:30 is
(a) 60°
(b) 45°
(c) 75°
(d) 90°

### Question. 2

The hour and the minute hands of a clock coincide at midnight. At what time of the day will the hands coincide again?

### Question. 3

After 12 noon the first right angle will be formed between the hands of a clock at
(a) 3 p.m.
(b) 3.16 p.m.
(c) 2.52 p.m.
(d) 2.40 p.m.

### Question. 4

Two clocks are set correctly at 10 a.m. on Friday. The first clock gains two minutes every hour, which is twice as much as the second. What time will be second clock register when the correct time is 2 p.m. on the following Monday?
(a) 3.22 p.m.
(b) 3.16 p.m.
(c) 2.52 p.m.
(d) 2.40 p.m.

### Question. 5

At how many minutes past 5 p.m. are the hands of a clock at right angles to one another between 5 p.m. and 6 p.m.?

(c) 10 min and 40 min
(d) None of these

### Question. 6

How much does a watch gain or lose per day if its hands coincide every 64 minutes of the correct time?
(a) Loses 90 minutes
(b) Gains 90 minutes

### Question. 7

At how many times pas 8 o’clock does the minute hands of a clock coincides with the hour hand between 8 p.m. and 9 p.m.?

### Question. 8

Find the time between 8 and 9 o’clock when the hands of a clock will be in a straight line in opposite direction.
(a)
(b) 12 min past 8
(c) 16 min past 8
(d) 11 min past 8

### Question. 9

At what time between 9 and 10 o’clock are the hands of a clock 5 minutes spaces apart?

### Question. 10

A clock is set right at 9 a.m. The clock gains 30 seconds per hour. What will be the true time when the clock indicates 3.39 p.m. on the 3rd-day afternoon?
(a) 4 p.m
(b) 3 p.m.
(c) 1 p.m.
(d) 2 p.m.

### Question. 11

A watch gains time uniformly. it was observed that it was 6 minutes slow at 12 o’clock in the night on Monday. On Friday at 12 o’clock in the night, it was 6 minutes 48 second fast. When was it correct?
(a) Wednesday, 6p.m.
(b) Wednesday, 7p.m.
(c) Thursday, 8 p.m.
(d) Wednesday, 9 p.m

## Solutions:

Hint:

#### Ans: 2 (B)

Hint:
If both the hands start moving together from the same position they will coincide after

Hint:

#### Ans: 4 (B)

Hint:
The second clock gains(24+24+24+4 minutes)

#### Ans: 5 (A)

Hint:
The hands of the clock will be at right angels after 5 p.m. once the minute hands has traversed 150° + 90°=240° over the minute hand.
Note that 330° are gained in 60 minutes.

#### Ans: 6 (D)

Hint:
in a correct watch, the minute hand gains 60 minutes over the hour hand (i.e. coincident) inminutes.

#### Ans: 7 (B)

Hint:
In order to be coincident the minute hand must traverse 240° over the hour hand

#### Ans: 8 (A)

Hint:
To be in a straight line the minute hand must traverse 60° over the hour hand.

#### Ans: 9 (A)

Hint:
5 minute spaces = 30°

Hint:

#### Ans: 11 (D)

Hint:

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