Would you please give here Concepts and formulas on clock topic in Quantitative Ability section for NMAT exam ?

As you want I am here giving you Concepts and formulas on clock topic in Quantitative Ability section for NMAT exam.

Concepts and formulas on clock topic in Quantitative Ability section:

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:
In 60 minutes, the minute hand gains 55 minutes on the hour 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 hands 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°.

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.

Sample questions :

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) 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.