Question 1
In a clock, the time is 3.25.What is the angle between the hour hand and the minute hand of the clock:
 A 95/2 degrees B 90/3 degrees C 94/3 degrees D 95/3 degrees
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Question 1 Explanation:
As, the hour hand covers 360 degrees in 12 hrs. In the clock the time is 3.25 = 3 hrs 25 min = 41/12 hrs. So, the angle traced by hour hand = (360/12 x 41/12) degrees = 205 degrees. The minute hand covers 360 degrees in 60 minutes. So, the angle is traced by minute hand in 25 min = (360/60 x 25) degrees = 150 degrees. Hence, the required angle of the clock = (150- 205/2) degrees = 95/2 degrees.
 Question 2
A clock gains uniformly 5 min slow at 8 o’clock in the morning on Sunday and 5 min 48 sec fast at 8 pm on following Sunday. The correct time and day are:
 A 21 min past 7 pm and Wednesday B 20 min past 7 pm and Thursday C 21 min past 7 pm and Thursday D 20 min past 7 pm and Wednesday
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Question 2 Explanation:
The given time from 8:00 am on Sunday to 8 pm on following Sunday = 7 days 12 hrs = 180 hrs. So, the clock gains = (5 + 29/5)min = 54/5 min in 180 hrs. Hence, 5 min are gained in (180 x 5/54 x 5)hrs = 83 hrs 20 min = 3 days 11 hrs 20 min. The clock is correct 3 days 11 hrs 20 min after 8 am of Sunday. So, the correct time and day will be 20 min past 7 pm on Wednesday.
 Question 3
Sam sets alarm at 5 am. But the clock loses 16 minutes in 24 hours. Effectively, the clock indicates 10:00 pm on the 4th day. Find out the original time of the clock:
 A 9 pm B 10 pm C 11 pm D 08 pm
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Question 3 Explanation:
From the given information the time from 5 am on a day to 10 pm on the 4th day is 89 hrs. So, 23 hrs 44 min of this clock = 24 hrs of correct clock. Hence, 356/15 hrs of this clock = 24 hrs of correct clock. 89 hrs of the clock = (24 x 15/356 x 89)hrs of correct clock = 90 hrs of correct clock. Hence, the original time will be 11 pm.
 Question 4
The time of a clock is 8 am. Suddenly the clock gains 10 minutes in 24 hours. Find out the original time if the time of the clock is 1 pm on the following day:
 A 48 minutes past 12 B 47 minutes past 10 C 48 minutes past 11 D 48 minutes past 11
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Question 4 Explanation:
From 8 am on a day to 1 pm on the following day will be 29 hrs. So, the clock gains 10 min in 24 hours = 24 hrs of the correct time. Hence, 145/6 hrs of the clock = 24 hrs of the correct clock. 29 hrs of the clock = (24 x 6/145 x 24)hrs of the correct clock = 28 hrs 48 min of the correct clock. The correct time = 28 hrs 48 min after 8 am. Hence, the original time is 48 minutes past 12.
 Question 5
A time of a clock is set 3.40. Find out the angle that is formed by both hour hand and minute hand:
 A 120 degrees B 135 degrees C 140 degrees D 130 degrees
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Question 5 Explanation:
The hour hand covers the angle 360 degrees in 12 hrs. So, the angle is covered by it in 11/3 hrs = (360/2 x 11/3) degrees = 110 degrees . The minute hand covers the angle in 360 degrees in 60 min. So, the angle is covered by it in 40 min = (360/60 x 40) degrees = 240 degrees . Hence, the required angle made by both hands = (240 - 110) degrees = 130 degrees .
 Question 6
A clock shows 8:00 AM. When it is 2:00 PM, by what degree the hour hand rotates?
 A 145º B 160º C 180º D 175º
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Question 6 Explanation:
For 6 hrs duration hrs hand covered 6 hrs out of 12 hrs
When hrs hand covers 12 hrs it rotates for 360 degree
----------------------------6 --------------------- = (360/12)*6 = 180 degrees
 Question 7
A clock shows 10:00 AM. When it is 4:00 PM, by what degree the hour hand rotates?
 A 140º B 152º C 175º D 180º
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Question 7 Explanation:
For 6 hrs duration hrs hand covered 6 hrs out of 12 hrs When hrs hand covers 12 hrs it rotates for 360 degree ----------------------------6 --------------------- = 360/12)*6 = 180 degrees
 Question 8
A clock shows 10:00 AM. When it is 10:00 PM, by what degree the hour hand rotates?
 A 180 B 175 C 240 D 360
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Question 8 Explanation:
For 6 hrs duration hrs hand covered 12 hrs out of 12 hrs When hrs hand covers 12 hrs it rotates for 360 degree ----------------------------12 --------------------- =(360/12)*12 = 360 degrees
 Question 9
A clock shows 10:00 AM. What time it will be showing, if hrs hand rotates for 180 degrees?
 A 1:00 PM B 6:00 PM C 4:00 PM D 10:00 PM
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Question 9 Explanation:
When hrs hand rotates for 360 degree it covers 12 hrs --------------------------------- 180 --------------------- 6 hrs So the time will be: 10:00 AM + 6 hrs = 4:00 PM
 Question 10
A clock shows 06:00 AM. What time it will be showing, if hrs hand rotates for 360 degrees?
 A 4:00 AM of next day B 06:00 PM C 04:00 PM D 10:00 PM
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Question 10 Explanation:
When hrs hand rotates for 360 degree it covers 12 hrs --------------------------------- 360 --------------------- 12 hrs So the time will be: 06:00 AM + 12 hrs = 06:00 PM
 Question 11
A clock shows 08:00 AM. What time it will be showing, if hrs hand rotates for 540 degrees?
 A 2:00 AM of next day B 4:00 PM C 4:35 PM D 01:00 AM of next day
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Question 11 Explanation:
When hrs hand rotates for 360 degree it covers 12 hrs After 360 degrees rotation clock will be showing 08:00 PM Remaining = 540-360 = 180 degrees So in 180 degrees it will cover 6 hrs So the time will be: 08:00 PM + 6 hrs = 02:00 AM of next day
 Question 12
The reflex angle between the hands of a clock at 09.25 is:
 A 200 degrees B 220.7 degrees C 182 degrees D 227.5 degrees
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Question 12 Explanation:
Reflex angle: The angle which has a measure between 180 and 360 degrees are called a Reflex Angle. Angle traced by hrs hand in 9 25/60  = 113/12 hrs =  (360/12)*(113/12) = 282.5 degrees Angel traced by minutes hand in 25 minutes = (360/60)*25 = 150 degrees
• Reflex angle = 360 – (282.5 – 150) = 227.5 degrees
 Question 13
A clock is started at 12:00 AM. The hrs hand rotates by how many degrees by 10 minutes past 5?
 A 240 B 175 C 155 D 180
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Question 13 Explanation:
Angle traced by hrs hand in 12 hrs = 360 degrees Angle traced by hour hand in 5 hrs 10 min. (5 10/60 hrs = 31/6 hrs)  =  (360/12)*(31/6) = 155 degrees
 Question 14
A faulty clock gains 5 seconds in every 3 minutes. Ram set it right at 8:00 AM. What is the true time when the clock indicates quarter past 5 o’clock of afternoon?
 A 4:30 PM B 7:00 PM C 5 :00 PM D 3:00 PM
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Question 14 Explanation:
quarter past 4 o’clock of afternoon is 5:15 PM Time duration from 8:00 AM to 5:15 PM = 37/4 hrs 3 min 5 sec of this clock means = 3 min of correct time 3 min 5 sec. = 37/720 hrs 3 min = 1/20 hrs
• 37/720 hrs of this clock = 1/20 hrs of correct time
• 37/4 hrs of this clock = (1/20)*(37/4)/(37/720) = 9 hrs of correct time
• So the correct time = 8:00AM + 9 hrs = 5 PM
 Question 15
At what time will the hrs hand and minute hand will be pointing just opposite to each other between 7:00 AM and 8:00 AM?
 A 60/12 minutes past 7:00 AM B 40/11 minutes past 7:00 AM C 60/11 minutes past 8:00 AM D 60/11 minutes past 7:00 AM
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Question 15 Explanation:
Both hands will be 30 min. space apart At 7:00 AM, they are 25 min space apart
• Minute hand will have to gain only 5 min spaces
55 min spaces are gained in 60 min
• 5 min spaces will be gained in 60/11 minutes
• Required time = 60/11 minutes past 7:00 AM
 Question 16
At what time between 6 am and 7 am will the minute hand and the hour hand of a clock make an angle closest to 60°?
 A 6:22 am B 6:27 am C 6:38 am D 6:45 am
Clocks
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Question 16 Explanation:
Angular speed of hour hand = 360/12 = 30° per hour = 30/60 = 0.5° per minute. Angular speed of minute hand = 360/60 = 6° per minute. Relative speed of hour hand and minute hand = 6 – 0.5 = 5.5° per minute. Angle between hour and minute hand at 6 AM = 180°. To make an angle of 60°, total angular distance will be = 180° - 60° = 120°. Time needed to cover angular distance of 120° by relative angular speed = 120°/5.5 = 21.81 minute. Hence closest time to make an angle of 60° = 6:22 AM.
There are 16 questions to complete.

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