Aptitude sums on Clock

Introduction

Aptitude makes you easy when you try those sums with the help of Nithra Jobs site. Learn clock problems with solutions that are given below with both questions and answers.

Formulas to use

1. Minute Spaces

The face or dial of clock 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 and the larger one is called minute hand or long hand.

2. i) In 60 minutes, minute hand gains 55 minutes on the hour over the hour hand.

ii) Both the hands of a clock coincide once in every hour.

iii) The hands of a clock are in the same straight line when they are coincident or opposite to each other.

iv) When the two hands of a clock are at right angles, they are 15 minute spaces apart.

v) When the hands of a clock are in opposite directions, they are 30 minute spaces apart.

vi) Angle traced by hour hand in 12 hrs = 360°

vii) Angle traced by minute hand in 60 min = 360°

viii) If a watch or a clock indicates 9.15, when the correct time is 9, 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.

ix) The hands of a clock will be in straight line but opposite in direction, 22 times in a day.

x) The hands of a clock coincide 22 times in a day.

xi) The hands of a clock are straight 44 times in a day.

xii) The hands of a clock are at right angles 44 times in a day.

Solved Problems

1. Find the angle between the hour hand and the minute hand of a clock when time is 2.25.

Answer: 77 (1/2) °

Explanation:

Angle traced by the hour hand in 12 hours = 360° 2 hr 25 min = 2 ( 25/60 )

= 145 / 60

= 29 / 12

Angle traced by it in 2 hour 25 min ( 29 / 12 hr) = ( 360 / 12 ) × ( 29 / 12 )

= 30 × ( 29 / 12 )

= 5 × ( 29 / 2 )

= 145 / 2

= 72 (1/2)°

Angle traced by it in 25 min = [ ( 360 / 60 ) × 25 ]°

= 6 × 25

= 150°

Required angle = 150° - 72 ((1/2))°

= 77 (1/2)° Required angle = 77 (1/2)°

2. An accurate clock shows 8?o clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 1?o clock in the afternoon?

Answer: 150°

Explanation:

Time Between 8AM to 1 PM = 5 hours

Angle traced by the hour hand in 12 hours = 360°

Angle traced by the hour hand in 5 hours = [ ( 360 / 12 ) × 5 ]°

= 30 × 5

= 150°

Required angle = 150°

3. The reflex angle between the hands of a clock at 10 is:

Answer: 60°

Explanation:

Angle traced by the hour hand in 12 hours = 360°

Angle traced by the hour hand in 10 hours = [ (360 / 12) × 10] °

= (30 × 10) °

= 300°

Reflex angle = 360° - 300°

= 60°

Reflex angle = 60°

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

Answer: 155°

Explanation:

Angle traced by hour hand in 12 hours = 360° 5 hr 10 min = 5 (10/60)

= 5 (1/6)

= 31 / 6

Angle traced by hour hand in 31 / 6 hour = ( 360 / 12 ) × ( 31 / 6 )

= 5 × 31

= 155°

Required angle = 155°

5. Find the angle between the hour hand and the minute hand of a clock when time is 6?

Answer: 180°

Explanation:

Angle traced by the hour hand in 12 hours = 360° Angle traced by it in 6 hours = ( 6 / 12 ) × 360°

= 6 × 30°

= 180°

Angle traced by it in 6 hours = 180°

Conclusion

Candidates can score marks in the clock reasoning section, So practice the concept of this section with different types of questions that are given in Nithra Jobs site.