Clock Reasoning Questions

Q-26. At what time between 6 to 7 O’ clock minute and hour hand will be at right angle or makes 90° angle ?
(a) 6 : 38\frac{2}{11}, 6:43 \frac{7}{11}
(b) 6:43 \frac{7}{11}, 6:49 \frac{1}{11}
(c) 6 : 49\frac{1}{11}, 6:16\frac{4}{11}
(d) 6: 16\frac{4}{11}, 6:54\frac{6}{11}

View Answer and Solution 

Answer: (c) 6 : 49\frac{1}{11}, 6:16\frac{4}{11}
Solution:
By unique Formula
= H :  \left ( H \times 5\pm \frac{Angle}{6} \right )\times \frac{12}{11}
H = 6, Angle = 90°
= 6:  \left ( 6 \times 5\pm \frac{90}{6} \right )\times \frac{12}{11}
= 6: \left ( 30\pm 15 \right )\times \frac{12}{11}
= 6: \left ( 30\dotplus 15 \right )\times \frac{12}{11}
= 6: \left ( 30 - 15 \right )\times \frac{12}{11}
= 6:25 x \frac{12}{11}, 6 : 15x \frac{12}{11}
= 6:\frac{540}{11}, 6: \frac{180}{11}
= 6:49\frac{1}{11}, 6:16 \frac{4}{11}
 

Q-27. At what time between 3 to 4 O’clock minute and hour hand are opposite to each other?
(a) 3 : 43\frac{7}{11}
(b) 3 : 38\frac{2}{11}
(c) 3 : 49\frac{1}{11}
(d) 3: 54\frac{6}{11}

View Answer and Solution 

Answer: (c) 3 : 49\frac{1}{11}
Solution:
By unique Formula
= H :  \left ( H \times 5\pm \frac{Angle}{6} \right )\times \frac{12}{11}
H = 3, Angle = 180°
Note: Hands are opposite means 180°
= 3:  \left ( 3 \times 5\pm \frac{180}{6} \right )\times \frac{12}{11}
= 3: \left ( 15\pm 30 \right )\times \frac{12}{11}
= 3: \left ( 15\dotplus 30 \right )\times \frac{12}{11}, 3: \left ( 15 - 30 \right )\times \frac{12}{11}
= 3:45 x \frac{12}{11}, 3 : (-15)x \frac{12}{11}
= 3:\frac{540}{11}, 3: \frac{-180}{11}
Angle = 180°
= 3:49\frac{1}{11}
 

Q-28. When did the minute and hour hand makes 180° angle between 6 to 70′ clock?
(a) 6: 54\frac{6}{11} (b) 6:60
(c) 6:00 (d) 6:5\frac{5}{11}

View Answer and Solution 

Answer: (c) 6:00 
Solution:
By unique Formula
= H :  \left ( H \times 5\pm \frac{Angle}{6} \right )\times \frac{12}{11}
H = 6, Angle = 180°
Note: Hands are opposite means 180°
= 6:  \left ( 6 \times 5\pm \frac{180}{6} \right )\times \frac{12}{11}
= 6: \left ( 30\pm 30 \right )\times \frac{12}{11}
= 6: \left ( 30\dotplus 30 \right )\times \frac{12}{11}, 6: \left ( 30 - 30 \right )\times \frac{12}{11}
= 6:60 x \frac{12}{11}, 6 : (0)x \frac{12}{11}
= 6:\frac{720}{11}, 6:00
Not Possible
Note: minute and hour hand does not make 180° angle between 5 to 6 and 6 to 7 O' clock.
 

Q-29. At what time between 8 to 9 O’ clock the minute and hour will apart 7 minutes to each other?
(a) 8:42, 8:51\frac{3}{11}
(b) 8: 36, 8:51\frac{3}{11}
(c) 8:09, 8:47\frac{4}{11}
(d) 8: 7, 8: 28\frac{9}{11}

View Answer and Solution 

Answer: (b) 8: 36, 8:51\frac{3}{11}
Solution:
\frac{Angle}{6}= minutes
By unique Formula
= H :  \left ( H \times 5\pm \frac{Angle}{6} \right )\times \frac{12}{11}
= 8:  \left ( 8 \times 5\pm 7 \right )\times \frac{12}{11}
= 8: \left ( 40\pm 7 \right )\times \frac{12}{11}
= 8: \left ( 40\dotplus 7 \right )\times \frac{12}{11}, 8: \left ( 40 - 7 \right )\times \frac{12}{11}
= 8:47 x \frac{12}{11}, 8 : 33 x \frac{12}{11}
= 8:\frac{564}{11}, 8: \frac{396}{11}
= 8:51\frac{3}{11}, 8:36

Q-30. The minute hand of a clock overtakes the hour hand at intervals of 64 minutes of correct time. How much a day does the clock gain or lose?
(a) 43\frac{9}{11}minute loss
(b) 32\frac{8}{11}minute gain
(c) 33\frac{9}{11}minute gain
(d) 32\frac{8}{11}minute loss

View Answer and Solution 

Answer: (b) 32\frac{8}{11}minute gain
Solution:
Normal watch overtakes in
= 65\frac{5}{11} minute
This watch overtakes in = 64 minute
It means In 64 minutes the clock gains
=65\frac{5}{11} - 64
= 1\frac{5}{11} = \frac{16}{11} min
“In one day = 24 × 60 minutes”
Then in 1 minute clock gains
= \frac{16}{11\times 64}
In 24 × 60 Minute clock gains
=\frac{16\times 24\times 60 }{11\times 64}
= \frac{360}{11} minutes
= 32\frac{8}{11} minutes