FACTS  AND  FORMULAE  FOR  CLOCKS  QUESTIONS

 

 

The face or dial of a watch is a circle whose circumference is divided into 6 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.

 

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

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

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

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

5. When the hands are in opposite directions, they are 30 minute spaces apart.

6. Angle traced by hour hand in 12 hrs = 360°

7. Angle traced by minute hand in 60 min. = 360°.

 

Too Fast And Too Slow : If a watch or clock indicated 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.

Q:

In every 60 minutes, the minute hand gains -------- minutes on the
hour hand

A) 53 B) 54
C) 55 D) 56
 
Answer & Explanation Answer: C) 55

Explanation:

point to be remembered

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26 17410
Q:

At 3.40, the hour hand and the minute hand of a clock form an angle of:

A) 110 B) 120
C) 130 D) 140
 
Answer & Explanation Answer: C) 130

Explanation:

Angle traced by hour hand in 12 hrs. = 360º. 

 

Angle traced by it in 113hrs =36012×11301100 

 

Angle traced by minute hand in 60 min. = 3600 

 

Angle traced by it in 40 min = 36060×4002400 

 

Required angle (240 - 110)º = 1300

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20 12397
Q:

The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:

A) 0 B) 10
C) 30 D) 60
 
Answer & Explanation Answer: B) 10

Explanation:

Angle traced by hour hand in 133hrs = 36012×13301300 

Angle traced by min. hand in 20 min = 36060×200 =1200 

Required angle = (130 - 120)º = 10º

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23 12206
Q:

When the hands are in the opposite directions,they are ------- minute spaces apart,

A) 15 B) 30
C) 60 D) 0
 
Answer & Explanation Answer: B) 30

Explanation:
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24 11308
Q:

What is the ratio of 18 minutes to one hour ?

A) 1/5 B) 3/4
C) 1/7 D) 3/10
 
Answer & Explanation Answer: D) 3/10

Explanation:

One hour = 60 min

18/60 = 3/10

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44 10334
Q:

How many minutes does a watch lose per day, if its hands coincide every 64 minutes ?

A) 36 7/9 min B) 32 8/11 min
C) 34 3/11 min D) 65 5/11 min
 
Answer & Explanation Answer: B) 32 8/11 min

Explanation:

55 min. spaces are covered in 60 min.

60 min. spaces are covered in open parentheses 60 over 55 cross times 60 close parentheses min. = 65 5 over 11 min.

Loss in 64 min. = open parentheses 65 5 over 11 minus 64 close parentheses equals 16 over 11 min.

Loss in 24 hrs = open parentheses 16 over 11 cross times 1 over 64 cross times 24 cross times 60 close parentheses min. = 32 8 over 11 min.

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38 10334
Q:

The angle between the minute hand and the hour hand of a clock when the time is 4.15 is

A) 0 B) 37.5
C) 27 D) 15
 
Answer & Explanation Answer: B) 37.5

Explanation:

Angle between hands of a clock

 

When the minute hand is behind the hour hand, the angle between the two hands at M minutes past H 'o clock

 

=> 30H-M5+M2 degrees

 

Here H = 4, M = 15 and the minute hand is behind the hour hand.

 

Hence the angle

 

 = 30[4-(15/5)]+15/2 = 30(1)+7.5 = 37.5 degrees

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28 9688
Q:

A watch which gains uniformly is 2 minutes low at noon on monday and is 4 min.48 sec fast at 2 p.m on the following monday. when was it correct ?

A) 2 p.m on Tuesday B) 2 p.m on Wednesday
C) 3 p.m on Thursday D) 1 p.m on Friday
 
Answer & Explanation Answer: B) 2 p.m on Wednesday

Explanation:

Time from 12 p.m on monday to 2 p.m on the following monday = 7 days 2 hours = 170 hours

 

Therefore, The watch gains 2+445 min. or  34/5 min. in 170 hrs.

 

Now, 34/5 min. are gained in 170 hrs.

 

Therefore, 2 min are gained in 170×534×2 hrs = 50 hrs

 

Therefore, Watch is correct 2 days 2 hrs. after 12 p.m on monday i.e it will be correct at  2 p.m on wednesday.

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