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:

At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but,not together?

A) (5 + 5/11 )min past 7 B) (6 + 5/11) min past 7
C) 7 D) 8
 
Answer & Explanation Answer: A) (5 + 5/11 )min past 7

Explanation:

When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.
At 7 o'clock, they are 25 min. spaces apart.
Minute hand will have to gain only 5 min. spaces.
55 min. spaces are gained in 60 min.

 

5 min spaces are gained in 6055*5 min  = 5511min 

 

so, Required time = 5511 min  past 7

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Q:

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

A) 360 B) 180
C) 90 D) 60
 
Answer & Explanation Answer: B) 180

Explanation:

Angle traced by the hour hand in 6 hours=(360/12)*6

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204 65580
Q:

At what time between 9 and 10 o'clock will the hands of a watch be together?

A) (49 + 3/11) min past 11 B) (49 +1/11) min past 9
C) (45 +1/11) min past 9 D) (45 +7/11) min past 11
 
Answer & Explanation Answer: B) (49 +1/11) min past 9

Explanation:

To be together between 9 and 10 o'clock, the minute hand has to gain 45 min. spaces.
55 min. spaces gained in 60 min.

 

45 min. spaces are gained in 6055×45 min  or 49111min

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Q:

At what time between 5.30 and 6 will the hands of a clock be at right angles?

A) (43 + 5/11) min past 5 B) (43 + 7/11) min pats 5
C) 5 D) 7
 
Answer & Explanation Answer: B) (43 + 7/11) min pats 5

Explanation:

At 5 o'clock, the hands are 25 min. spaces apart.
To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.

 

55 min. spaces are gained in 60 min

 

40 min. spaces are gained in 6055×40 min  

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Q:

A watch gains 5 seconds in 3 minutes and was set right at 8 AM. What time will it show at 10 PM on the same day ?

A) 10 : 27 : 41 AM B) 8 : 51 : 04 AM
C) 9 : 45 : 15 PM D) 10 : 23 : 20 PM
 
Answer & Explanation Answer: D) 10 : 23 : 20 PM

Explanation:

The watch gains 5 seconds in 3 minutes = 100 seconds in 1 hour.

From 8 AM to 10 PM on the same day, time passed is 14 hours.

In 14 hours, the watch would have gained 1400 seconds or 23 minutes 20 seconds.

So, when the correct time is 10 PM, the watch would show 10 : 23 : 20 PM

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Q:

What time between 4 and 5 o'clock will the hands of a clock be at rightangle?

A) 3 5/11 B) 4 5/11
C) 5 5/11 D) 6 5/11
 
Answer & Explanation Answer: C) 5 5/11

Explanation:

this type of problems the formulae is
(5*x + or -15)*(12/11)
Here x is replaced by the first interval of given time
here i.e 4
Case 1 : (5*x + 15)*(12/11)
(5*4 +15)*(12/11)
(20+15)*(12/11)
35*12/11=420/11=38 2/11 min.
Therefore they are right angles at 38 2/11 min .past4
Case 2 : (5*x-15)*(12/11)
(5*4-15)*(12/11)
(20-15)*(12/11)
5*12/11=60/11 min=5 5/11min
Therefore they are right angles at 5 5/11 min.past4.

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Q:

At what time between 3 and 4 o’clock will the minute hand and the hour hand are on the same straight line but facing opposite directions ?

A) 3:15 2/8 B) 3:49
C) 3:49 1/11 D) 3:51
 
Answer & Explanation Answer: C) 3:49 1/11

Explanation:

On straight line means 180 degree angle.
180 = 11/2 min – 30 hrs
180 = 11/2 m – 30 × 3
180 = 11/2 m – 90
(180 + 90) 2 = 11 m
m = 540/11 = 49 1/11 minutes.

 

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49 39801
Q:

In 16 minutes, the minute hand gains over the hour hand by -

A) 16 deg B) 80 deg
C) 88 deg D) 94 deg
 
Answer & Explanation Answer: C) 88 deg

Explanation:

In one hour, the minute hand gains 330° over the hour hand. i.e., 60 minute, the minute hand gains 330° over the hour hand.

∴ In 16 minutes, the minute hand gain over the hour hand by fraction numerator 330 degree over denominator 60 end fraction cross times 16 degree equals 88 degree

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