**CAT 2021: Quantitative Ability – Important Concepts and Formulas on Clock**

CAT 2021 will be conducted in November 2021. Following understanding on concepts and formulas on clock will help you in Quantitative Ability section:

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**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.

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

ii. In every hour, both the hands coincide once.

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

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

v. When the hands 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 8.15, when the correct time is 8, it is said to be 15 minutes too fast.

ix. On the other hand, if it indicates 7.45, when the correct time is 8, it is said to be 15 minutes too slow.

**Illustrations:**

**Q)**Find the angle between the minute hand and hour hand of a click when the time is 7.20?

**Ans**: 100deg.

**Sol:**

• Angle traced by the hour hand in 12 hours = 360 degrees.

• Angle traced by it in 7 hrs. 20 min i.e. 22/3 hrs. = [(360/12) * (22/3)] = 220 degrees

• Angle traced by minute hand in 60 min = 360 deg.

• Angle traced by it in 20 min = [(360/20) * 60] = 120 deg.

• Therefore, required angle = (220 - 120) = 100deg.

**Q)**The minute hand of a clock overtakes the hours hand at intervals of 65 min of the correct time. How much of the day does the clock gain or lose?

**Ans**: the clock gains 10 10/43 minutes

Sol:

• In a correct clock, the minute hand gains 55 min. spaces over the hour hand in 60 minutes. To be together again, the minute hand must gain 60 minutes over the hour hand.

• 55 minutes are gained in 60 min.

• 60 min. are gained in [(60/55) * 60] min = 65 5/11 min.

• But they are together after 65 min.

• Therefore, gain in 65 minutes = (65 5/11 - 65) = 5/11 min.

• Gain in 24 hours = [(5/11) * (60*24)/65] = 10 10/43 min.

• Therefore, the clock gains 10 10/43 minutes in 24 hours.

**Q)**A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours. What will be the true time when the clock indicates 1 p.m. on the following day?

**Ans.**48 min. past 12.

**Sol:**

• Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hours.

• 24 hours 10 min. of this clock = 24 hours of the correct clock.

• 145/6 hrs of this clock = 24 hours of the correct clock.

• 29 hours of this clock = [24 * (6/145) * 29] hrs of the correct clock

• = 28 hrs 48 min of the correct clock.

• Therefore, the correct time is 28 hrs 48 min. after 8 a.m.

• This is 48 min. past 12.

**Q)**At what time between 2 and 3 O’ clock will the hands of a clock together?

**Ans:**10 10/11 min. past 2.

**Sol:**

• At 2 O’ clock, the hour hand is at 2 and the minute hand is at 12, i.e. they are 10 min space apart. To be together, the minute hand must gain 10 minutes over the other hand. Now, 55 minutes are gained by it in 60 min.

• Therefore, 10 min will be gained in [(60/55) * 10] min = 10 10/11 min.

• Therefore, the hands will coincide at 10 10/11 min. past 2.

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