Aptitude ➤ Clocks ➤ Set 1

#### Clocks : Important Facts and Formulae

Minute Spaces:
The face or dial of watch is a circle whose circumference is divided into 60 equal parts, called minute spaces.

Hour Hand and Minute Hand:
A clock has two hands, the smaller one is called the hour hand or short hand while the larger one is called minute hand or long hand.

(a) In 60 minutes, the minute hand gains 55 minutes on the hour on the hour hand.
(b) In every hour, both the hands coincide once.
(c) The hands are in the same straight line when they are coincident or opposite to each other.
(d) When the two hands are at right angles, they are 15 minute spaces apart.
(e) When the hands are in opposite directions, they are 30 minute spaces apart.
(f) Angle traced by hour hand in 12 hrs = 360°
(g) Angle traced by minute hand in 60 min. = 360°.

Too fast And Too Slow :
If a watch or a clock indicates 8.15, when the correct time is 8, it is said to be 15 minutes too fast.
On the other hand, if it indicates 7.45, when the correct time is 8, it is said to be 15 minutes too slow.
Question 1
Q1.  An accurate clock shows 8 O'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 O'clock in the afternoon?
Question 2
Q2.  How many times are the hands of a clock at right angle in a day?
Question 3
Q3.  How many times in a day, are the hands of a clock in straight line but opposite in direction?
Question 4
Q4.  Find the angle between the hour hand and the minute hand of a clock when the time is 3.25.
Question 5
Q5.  At what time, in minutes, between 3 O'clock and 4 O'clock, both the needles will coincide each other?