1.
At what time between 5 and 6 o'clock. The hands of a clock coincident
•  A. 27 3 min. past 5 11
•  C. 26 1 min. past 5 4
• B.
27 min. past 5
•  D. 25 1 min. past 5 2
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Explanation :
At 5 o�clock the hour hand is at 5 and the minute hand is at 12, (i.e) they are 25 min spaces apart.
To be together, the minute hand must gain 25 minutes over the hour hand.
25 minutes will be gained in =
 60 55
x 25 =
 12 11
x 25 =
 300 11
= 27
 3 11
min.
The hands will coincide at 27
 3 11
min. past 5.
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2.
At what time between 12 and 1 o'clock both the hands will be at right angles?
•  A. 540 min. past 12 11
•  C. 150 min. past 12 11
•  C. 180 min. past 5 11
• D.
Both a) and b)
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Explanation :
At 12 o�clock the minute hand and hour hand coincide (i.e) they are 0° apart.
Now, when the two hands are at right angles, they are 15 min.
spaces apart. So they are at right angles in following 2 cases:
Case (i) When minute hand is 15 min. spaces behind the hour hand:
In this case, minute hand will have to gain 15 � 0 = 15 minutes spaces
55 minutes spaces are gained in = 60 min.
15 minutes spaces will be gained by it in =
 60 55
x 15 =
 180 11
min.
They are at right angles at =
 180 11
min. past 12.
Case (ii) When the minute hand is 15 min. spaces ahead of the hour hand:
The similar right angle occurs at =
 180 11
x 3 =
 540 11
min. past 12.
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3.
A clock is set right at 1 p.m. If it gains one minute an hour, what is the true time when the clock indicates 6 p.m. on the same day?
•  A. 4 56 min. past 5 p.m 61
•  C. 55 5 min. past 5 p.m 61
•  B. 42 56 min. past 5 p.m 61
•  D. 52 4 min. past 5 p.m 5
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Explanation :
Total number of hours from 1 p.m to�6 p.m on the same day = 5 hours
The clock gains 1 min in 1 hour
It gains 24 min. in 24 hours
24 hrs in 24 min. in 24 hours
24 hrs 24 min. of this clock = 24 hrs of correct clock

 122 5
hrs. of this clock = 24 hrs of the correct clock
5 hrs of this clock = 24 x
 5 122
x 5 = 4
 56 61
hrs. of correct time
The correct time is 4
 56 61
hrs. after 1 p.m.
= 5 p.m and
 56 61
x 60 min. = 5 p.m. and
 3360 61
min.
= 5 p.m and 55
 5 61
min. (i.e) 55
 5 61
min. past 5 p.m.
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4.
At what time between 7 and 8 o'clock will the angle between the two hands of a clock be 0°?
• A.
7.36
• C.
7.35
• B.
7.40
• D.
7.38
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Explanation :
At 7 o'clock the hour hand is at 7 and the minute hand is at 12, (i.e) they are 35 min. spaces apart.
To be together, the minute hand must gain 35 min. over the hour hand.
55 min are gained in 60 min.
25 min. will be gained in =
 60 55
x 35
=
 12 11
x 35 =
 420 11
= 38
 2 11
min.
(i.e.) 38
 2 11
min. past 7. (i.e.) = 7.38
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