Clock Reasoning Questions with solution

Q-21. What is the angle between minute and hour hand at 3 : 56?
(a) 152° (b) 228°
(c) 360° (d) 142°

View Answer and Solution 

Answer: (d) 142°
Solution:
Formula For Angle
= H x 30 = F°
H=3 , M= 56
3 x 30 = 90°
56x \frac{11}{2}=308°
308°-90°=218°
But275°is more than 180° hence we subtract this angle from 360°
360° - 218° = 142°
 

Q-22. What is the angle between minute and hour hand at 12:20?
(a) 260° (b) 110°
(c) 120° (d) 20°

View Answer and Solution 

Answer: (b) 110°
Solution:
Formula For Angle
= H x 30 = F°
H=12 , M= 20
12 x 30 = 360°
20x \frac{11}{2}=110°
360°-110°=250°
But250°is more than 180° hence we subtract this angle from 360°
360° - 250° = 110°
 

Q-23. At what time between 6 to 7 O’ clock minute and hour hand will coincide?
(a) 6 : 38\frac{2}{11}
(b) 6 : 43\frac{7}{11}
(c) 6:32\frac{8}{11}
(d) 6:5\frac{5}{11}

View Answer and Solution 

Answer: (c) 6:32\frac{8}{11}
Solution:
Coincide means 0° Angle
By unique Formula
= H :  \left ( H \times 5\pm \frac{Angle}{6} \right )\times \frac{12}{11}
Angle = 0°, h = 6 then,
= 6:  \left ( 6 \times 5\pm \frac{0}{6} \right )\times \frac{12}{11}
= 6: \left ( 30\pm 0 \right )\times \frac{12}{11}
= 6: \frac{360}{11}
= 6: 32 \frac{8}{11}
 

Q-24. At what time between 10 to 11 O’clock minute and hour hand will coincide or makes O° angle?
(a) 10:43\frac{7}{11}
(b) 10:38\frac{2}{11}
(c) 10:54\frac{6}{11}
(d) 10: 10\frac{10}{11}

View Answer and Solution 

Answer: (c) 10:54\frac{6}{11}
Solution:
By unique Formula
= H :  \left ( H \times 5\pm \frac{Angle}{6} \right )\times \frac{12}{11}
H = 10, Angle = 0°
= 10:  \left ( 10 \times 5\pm \frac{0}{6} \right )\times \frac{12}{11}
= 10: \left ( 50\pm 0 \right )\times \frac{12}{11}
= 10: \frac{600}{11}
= 10: 54\frac{6}{11}
 

Q-25. At what time between 2 to 3 O’ clock minute and hour hand will be at right angle to each other or makes 90° angle
(a) 2 : 32 (b) 2 : 27
(c) 2 : 10 (d) 2 : 16

View Answer and Solution 

Answer: (b) 2 : 27
Solution:
By unique Formula
= H :  \left ( H \times 5\pm \frac{Angle}{6} \right )\times \frac{12}{11}
H = 2, Angle = 90°
= 2:  \left ( 2 \times 5\pm \frac{90}{6} \right )\times \frac{12}{11}
= 2: \left ( 10\pm 15 \right )\times \frac{12}{11}
= 2:(25) x \frac{12}{11}, 2 : (-5)x \frac{12}{11}
= 2:\frac{300}{11} 2: \frac{-60}{11}
This is not Possible 2:27\frac{3}{11}