# Clock Aptitude Formula, Clock Problem Shortcuts and Tricks

Clock Important Questions - Page 2
Clock Video Lecture - Page 3

Clock: 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 short hand while the larger one is called the minute hand or long hand.

## Clock Important Formulas

• 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 coincident or opposite to each other.
• When the two hands are at right angles, they are 15 minute spaces apart
• When the hand's are in opposite directions, they are 30 minute spaces apart
• Angle traced by hour hand in 12 hrs = 360°.
• 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 , 8 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.

## Solved Examples for Clock Problem

Question - 1: The angle between the minute hand and the hour hand of a clock when the time is 4 : 20

Solution: Angle traced by hour hand in $\frac{13}{3}$ hrs = $\left(\frac{360}{12}\times \frac{13}{3}\right )^{\circ}\; =\; 130^{\circ}$

Angle traced by min. hand in 20 min. = $\left (\frac{360}{60}\times 20\right )^{\circ}\; =\; 120^{\circ}$

$\therefore$ Required angle = (130 - 120)º = 10º.

Question - 2: How many times are the hands of a clock at right angle in a day?
Solution: In 12 hours, they are at right angles 22 times.

$\therefore$ In 24 hours, they are at right angles 44 times.

Question -3: How many times in a day, are the hands of a clock in straight line but opposite in direction?

Solution: The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o' clcok only).

So, in a day, the hands point in the opposite directions 22 times

Question - 4: At what time between 9 and 10 o'clock will the hands of a watch be together?
Solution: To be together between 9 and 10 o'clock, the minute hand has to gain 45 min. spaces. 55 min. spaces gained in 60 min.

45 min. spaces are gained in $\left (\frac{60}{55}\times 45\right)\; =\; 49\frac{1}{11}$ min

$\therefore$The hands are together at $49\frac{1}{11}$ min past 9

## One Response to “Clock Aptitude Formula, Clock Problem Shortcuts and Tricks”

1. Comment made by Rh karan on Oct 1st 2017 at 2:44 am: Reply

I want problems related to gaining or losing of clock