# How to Solve Clocks Question Quickly

## How to Solve Quickly Clocks & Definitions

A clock is a complete circle having an angle of 360 degrees. This circle is further divided into 12 equal parts  each part having 360/12 =  300. The minute hand takes one complete round in one hour covering an angle of 3600 in 60 minutes.

• The dial of the clock is circular in shape and is divided into 60 equal minute spaces.
•  60-minute spaces traces an angle of 3600. Therefore, one minute space traverses an angle of 600.
• Hands of a clock are in straight line and are opposite to one another when they are 30 minutes space apart.
• The complete clock circle has been divided into 12 equal bigger units also, which we call as hours. This further implies that every hour space covers a total of 360/12 = 30 degrees. ## Type 1: How To Solve Quickly Clocks

### Ques 1.

Calculate the angle between the two hands of a clock when the time shown by the clock is 7: 30 a.m.

Options:

A. 1000

B. 1550

C.2000

D. None of the above

#### Solution

From the formula

Angle = 11/2M – 30H, where M =30, and H =7

= 11/2*30 – 30 x 7

= |165 – 210|, taking the mode of the values, we get

= 1550

### Ques 2.

Calculate the degree at which the hour hand moves when the minute’s hand moves 750 times.

Options:

A. 130

B. 12*(3/6)°

C. 15(3/6)°

D. Cannot be determined

#### Solution:

Degrees covered by hour hand in one minute = 1/60

The minute hand will cover 750/60 degrees in 650 minutes.

This can be written as =   12 (3/6)° degrees.

### Ques 3.

What is the angle an hour hand has to trace when it covers the time from 8 A.M in the morning to 2 o’clock in the afternoon?

Options

A. 120

B.180

C.250

D. None of the above

#### Solution:

Time between 8 A.M to 2 P.M = 6 hours.

Therefore, the angle traced by the hour hand = 360/12 x 6

= 1800

## Type 2: Solve Quickly Clocks Ques.

### Ques 1.

Determine the time at which the minute and the hour hand will be in the same straight line facing opposite directions between 2 and 3 o’clock.

Options:

A. 2:43(7/11) P.M.

B. 2:45 P.M.

C.2:50(1/13) P.M.

D. None of the above

#### Solution:

Degrees in a straight line = 1800

When we apply the formula, 11/2M – 30H

=  (180+60)/2  = 11M

Or, M =43(7/11)

### Ques 2.

A clock is set to correct timing at 8 a.m. In the next 24 hours, it gains 10 minutes. What will be the true time when the clock displays time to be 1 P.M?

Options

A. 12: 48 P.M

B.  2:50 P.M.

C. 1: 30 A.M.

D. Cannot Be Determined

#### Solution:

Number of hours from 8 A.M on a day to 1 P.M the next day = 29

24 hours 10 minutes of this clock = 24 hours of a correct clock

145/6    hours of this incorrect clock = 24 hours of the correct clock

29 hours of incorrect clock = 24 x 6/145 x 29 hours of the correct clock

= 28 hours and 48 minutes of the correct clock

Therefore, the correct time is 28 hours and 48 minutes after 8 A.M

Which means, the true time will be 12:48 P.M.

### Ques 3.

What is the time between 4 and 5 o’clock, when the hands of the watch points in the opposite direction?

Options

A.  4:54 o’clock

B.  5 o’clock

C. 10 o’clock

D. Cannot be Determined

#### Solution:

Hands of the clock are 20 min. spaces apart when the time is 4 o’clock

They must be 30 min. Spaces apart to be in opposite directions.

Minute hand needs to gain 50 min. spaces

A clock gains 55 min. spaces in 60 minutes

50 min spaces are gained in

=  60/55 x 50 minutes

= 54(6/11)

The needed time = 54(6/11) past 4, or

= 4: 54