Quants 7 - Clocks

Key Points to Remember:

The face or dial of a watch is a circle whose circumference is divided into 60 equal parts, called minute spaces.
A clock has two hands. The smaller one is called, the hour hand or the short hand and the larger one is called the minute hand or the large hand.

In 60 minutes, the minute hand gains 55 minutes on the hour hand.
In every hour, both the hands, coincide once.
The hands are in the same straight line, when they are coinciding or on opposite to each other.
When the two hands are at right angles, they are 15 minute spaces apart.
When the hands are in opposite directions, they are 30 minute spaces apart.
Angle traced by hour hand in 12 hours = 360˚.
Angle traced by minute hand in 60 minutes = 360˚.

Too Fast and Too Slow - 
If the clock indicates 7.15, when the correct time is 7, it is said to be 15 minutes too fast.
If the clock indicates 6.45, when the correct time is 7, it is said to be 15 minutes too slow.

Practice Questions:

Question 1:

Find the angle between the hour hand and the minute hand of the clock when the time is 3.25.

Angle traced by the hour hand in 12 hours = 360˚.
Angle traced by it in 3.25 hours ie 3 (25/60) => 205/60 => 41/12 hrs = (360/12) * ( (41/12) = 205/2 = 102 (1/2)˚
Angle traced by minute hand in 60 minutes = 360˚.
Angle traced by it in 25 minutes = (360/60) * 25 = 150˚.
Required angle = 150˚ - 102 (1/2)˚ = 47 (1/2)˚.

Question 2:

A clock is started at noon. By 10 minutes past 5, the hour hand has turned through ___.

Angle traced by hour hand in 12 hours = 360˚.
Angle traced by hour hand in 5 hours 10 minutes i.e., 5(10/60) -> 31/6 hours = (360/12) * (31/6) = 155˚

Question 3:
At what time between 2 and 3 o'clock, will the hands of the clock be together?

At 2'o clock, the hour hand is at 2 and the minute hand is at 12, i.e., they are 10 minute spaces apart.
To be together, the minute hand must gain 10 minutes over the hour hand.
Now 55 minutes are gained by it in 60 minutes.
10 minutes will be gained in (60/55) * 10 = 120/11 = 10(10/11) minutes.
The hands will coincide at 10 10/11 minutes past 2.

Question 4:
An accurate clock shows 8 o'clock in the morning. Through how many degrees, will the hour hand rotate when the clock shows 2 o'clock in the afternoon?

Angle traced by hour hand in 6 hours (8.00 am to 2.00 pm) = 60 * 6 = 360˚.


Question 5:

The angle between the minute hand and the hour hand of a clock when the time is 8.30, is ___.

Angle traced by the hour hand in 12 hours = 360˚.
Angle traced by hour hand in 8.30 hours i.e., 17/2 hours = (360/12) * (17/2) = 255˚
Angle traced by minute hand in 60 minutes = 360˚.
Angle traced by minute hand in 30 minutes = (360/60) * 30 = 180˚
Required angle = 255˚ - 180˚ = 75˚


Time to Think:

At 3.40, the hour hand and the minute hand of the clock form an angle of ___.