6th Class Mental Ability Related to Competitive Exam Time and Clock

                                                                                    Time and Clock

Learning Objectives

• Time and Clock

Time and clock

Clock is a device which is used to measure and display the time. The face or dial of a clock is divided into 60 equal parts called minute space and it is numbered from 1 to 12, in such a way that each subsequent number is equidistant (5 minutes spaces apart) from the preceding number. A clock has two hands, the smaller one is the hour hand/ while larger one is called the minute hand. When hour hand travels five minutes spaces, the minute hand travels 60 minutes spaces. Therefore, in 60 minutes the minute hand gains 55 minute on the hour hand.

Properties of clock

• In 60 minutes/ the minute hand gains 55 minutes on the hour hand,
• A clock is said to be too fast, if it shows time more than that of shown by a correct clock.
• A clock is said to be too slow, if it shows time less than that of shown by a correct clock.
• In every hour, both the hands coincide once.
• When the two hands are at right angle, they are 15 minutes spaces apart.
• When the two hands are in opposite directions, they are 30 minutes spaces apart, this situation occurs once in a hour.
• The hands of a clock are in straight line when they are coincident or opposite to each other.
• Hour hand of a clock takes 12 hours to trace the angle of \[360{}^\circ \].
• Minute hand of a clock takes 1 hour to trace the angle of \[360{}^\circ \].

Example 1

Choose the time from the following options when the hands of a clock will be in the same straight line.

(a) 4:00 p.m.                           (b) 8:00 p.m.

(c) 7:00 p.m.                          (d) 6:00 p.m.

(e) None of these

Answer (d)

Explanation: The two hands of a clock are in the same straight line when they are either coincident or 30 minutes spaces apart from each other.

At 4:00 p.m., the minute hand will be 20 minutes spaces apart from the hour hand.

So option (a) is incorrect.

At 8:00 p.m., the minute hand will be 20 minutes spaces apart from the hour hand.

So option (b) is incorrect.

At 7:00 p.m., the minute hand will be 25 minutes spaces apart from the hour hand.

So option (c) is incorrect.

At 6:00 p.m., the minute hand will be 30 minutes spaces apart from the hour hand.

So option (d) is correct.

Therefore, the correct answer is 6 : 00 p.m.

Between 2 O'clock to 10 O'clock, how many times the hands of a clock are at right angle?

(a) 14                                      (b) 12

(c) 16                                       (d) 15

(e) None of these

Answer (a)

Explanation: Option (a) is correct. Between 2 and 4 O' clock, 8 and 10 O' clock, the hands are at right angle thrice in each case. Between 4 and 8'O clock, the hands are eight times at right angles.

So total number of times the hands are at right angles \[=3+3+\left( 2\times 4 \right)=14.\]

At what angle the hands of a clock are inclined when it is half past 8?

(a) \[75{}^\circ \]                 (b) \[70{}^\circ \]

(c) \[85{}^\circ \]                  (d) \[65{}^\circ \]

(e) None of these

Answer (a)

Explanation: Option (a) is correct. At half past 8 the minute hand points towards 6 and the hour hand points towards \[2\frac{1}{2}\] marks between 8 and 9. The angle between 6 and 8 is \[60{}^\circ \]and the angle \[2\frac{1}{2}\] min. space is \[15{}^\circ \]. Hence, total angle between two hands is \[75{}^\circ \].           

If the two hands in a clock are 5 minutes division apart, then the angle between them is?

(a) \[3{}^\circ \]                           (b) \[30{}^\circ \]

(c) \[24{}^\circ \]                       (d) \[60{}^\circ \]

(e) None of these

Answer (b)

Explanation: Option (&) is correct. In a clock, each minute makes \[6{}^\circ \].

So 5 minutes will make \[6\times 5=30{}^\circ .\]

The priest told the devotees, "The temple bell is rung at regular intervals of 45 minute. The last bell was rung five minutes ago. The next bell is due to be rung at 7:45 a.m”, At what time did the priest give this information’s to the devotees?

(a) 7:40 a.m.                  (b) 7:05 a.m.

(c) 7:00 a.m.                  (d) 6:55 a.m.

(e) None of these

Explanation: Option (b) is correct. It is clear from the information that the next bell is due to be rung at 7:45, and at regular Interval of 45 minute the bell is rung.

So, the previous bell was rung at \[7:45-00:45=7:00\] a.m, The priest told that the bell was rung five minutes ago, so the priest gave the information at \[07:00\text{ }a.m.+00:05\text{ }=7:05\text{ }a.m.\]

Commonly Asked Questions

Raman left home for the bus stop 15 minute earlier than usual, it takes 10 minutes to reach the stop. He reached the stop at 8:40 a,m. What time does he usually home for the bus stop?

(a) \[8:30\text{ }a.m.\]                (b) \[8:45\text{ }p.m.\]

(c) \[8:55\text{ }a.m.\]                 (d) \[8:45\text{ }a.m\]

(e) None of these

Explanation: Option (d) is correct. Raman reached bus stop at 8:40 a.m. and it takes 10 minutes to reach the stop so clearly he left his home at 8:30 a.m.

Raman left home 15 minutes earlier than usual, so he leaves his home for the bus stop usually at 8:30 + 0:15 = 8:45 a.m.

At what time, between 5 and 6 are the hands of a clock coincide?

(a) 22 minute past 5       

(b) 30 minute past 5

(c) \[22\frac{8}{11}\] minute past 5         

(d) \[27\frac{3}{11}\] minute past 5

(e) None of these

Answer (d)

Explanation: Option (d) is correct. From the figure given in the question we find that minute hand is 25 minute spaces apart from hour hand. In order to coincide it has to gain 25 minute spaces.

Now, 55 minute are gained by minute hand in 60 minute.

25 minute will be gained in \[\frac{60}{55}\times 25=27\frac{3}{11}\] minute.

So, the hands will coincide at \[27\frac{3}{11}\]minute past 5.

At what angle the hands of a clock are inclined at 15 minute past 5?

(a) \[72\frac{1}{2}{}^\circ \]                  

(b) \[67\frac{1}{2}{}^\circ \]

(c) \[58\frac{1}{2}{}^\circ \]                             

(d) \[64{}^\circ \]

(e) None of these

Answer (b)

Explanation: Option (b) is correct. At 15 minute past 5, the minute hand is at 3 and hour hand slightly ahead of 5.

Now, the angle through which hour hand shifts in 15 minute \[=\left( 15\times \frac{1}{2} \right){}^\circ =7\frac{1{}^\circ }{2}.\]

Angle at 15 minute past \[5=\left( 60+7\frac{1}{2} \right){}^\circ =67\frac{1{}^\circ }{2}.\]

Flights to Mumbai leave every 5 hours. At the information counter, I learnt that the flight took off 25 min before. If the time now is 10:45 a.m, what is the time for the next flight?

(a) \[4:10\text{ }a.m.\]                (b) \[2:20\text{ }a.m.\]

(c) \[4:20\text{ }p.m.\]                 (d) \[3:20\text{ }p.m.\]

(e) None of these

Answer (d)

Explanation: Option (d) is correct. Earlier flight took off at \[10:45-25\text{ }minutes=10:20\text{ }a.m.\] the next flight will be after 5 hours i.e., at 3:20 p.m.