50+ Clock Reasoning Questions and Answers
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[latex]\frac{2}{11}[/latex], 6:43 [latex]\frac{7}{11}[/latex]
(b) 6:43 [latex]\frac{7}{11}[/latex], 6:49 [latex]\frac{1}{11}[/latex]
(c) 6 : 49[latex]\frac{1}{11}[/latex], 6:16[latex]\frac{4}{11}[/latex]
(d) 6: 16[latex]\frac{4}{11}[/latex], 6:54[latex]\frac{6}{11}[/latex]
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Answer: (c) 6 : 49[latex]\frac{1}{11}[/latex], 6:16[latex]\frac{4}{11}[/latex]
Solution:
By unique Formula
= H : [latex] \left ( H \times 5\pm \frac{Angle}{6} \right )\times \frac{12}{11}[/latex]
H = 6, Angle = 90°
= 6: [latex] \left ( 6 \times 5\pm \frac{90}{6} \right )\times \frac{12}{11}[/latex]
= 6: [latex]\left ( 30\pm 15 \right )\times \frac{12}{11}[/latex]
= 6: [latex]\left ( 30\dotplus 15 \right )\times \frac{12}{11}[/latex]
= 6: [latex]\left ( 30 - 15 \right )\times \frac{12}{11}[/latex]
= 6:25 x [latex]\frac{12}{11}[/latex], 6 : 15x [latex]\frac{12}{11}[/latex]
= 6:[latex]\frac{540}{11}[/latex], 6: [latex]\frac{180}{11}[/latex]
= 6:49[latex]\frac{1}{11}[/latex], 6:16 [latex]\frac{4}{11}[/latex]
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Q-27. At what time between 3 to 4 O’clock minute and hour hand are opposite to each other?
(a) 3 : 43[latex]\frac{7}{11}[/latex]
(b) 3 : 38[latex]\frac{2}{11}[/latex]
(c) 3 : 49[latex]\frac{1}{11}[/latex]
(d) 3: 54[latex]\frac{6}{11}[/latex]
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Answer: (c) 3 : 49[latex]\frac{1}{11}[/latex]
Solution:
By unique Formula
= H : [latex] \left ( H \times 5\pm \frac{Angle}{6} \right )\times \frac{12}{11}[/latex]
H = 3, Angle = 180°
Note: Hands are opposite means 180°
= 3: [latex] \left ( 3 \times 5\pm \frac{180}{6} \right )\times \frac{12}{11}[/latex]
= 3: [latex]\left ( 15\pm 30 \right )\times \frac{12}{11}[/latex]
= 3: [latex]\left ( 15\dotplus 30 \right )\times \frac{12}{11}[/latex], 3: [latex]\left ( 15 - 30 \right )\times \frac{12}{11}[/latex]
= 3:45 x [latex]\frac{12}{11}[/latex], 3 : (-15)x [latex]\frac{12}{11}[/latex]
= 3:[latex]\frac{540}{11}[/latex], 3: [latex]\frac{-180}{11}[/latex]
Angle = 180°
= 3:49[latex]\frac{1}{11}[/latex]
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Q-28. When did the minute and hour hand makes 180° angle between 6 to 70′ clock?
(a) 6: 54[latex]\frac{6}{11}[/latex] (b) 6:60
(c) 6:00 (d) 6:5[latex]\frac{5}{11}[/latex]
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Answer: (c) 6:00
Solution:
By unique Formula
= H : [latex] \left ( H \times 5\pm \frac{Angle}{6} \right )\times \frac{12}{11}[/latex]
H = 6, Angle = 180°
Note: Hands are opposite means 180°
= 6: [latex] \left ( 6 \times 5\pm \frac{180}{6} \right )\times \frac{12}{11}[/latex]
= 6: [latex]\left ( 30\pm 30 \right )\times \frac{12}{11}[/latex]
= 6: [latex]\left ( 30\dotplus 30 \right )\times \frac{12}{11}[/latex], 6: [latex]\left ( 30 - 30 \right )\times \frac{12}{11}[/latex]
= 6:60 x [latex]\frac{12}{11}[/latex], 6 : (0)x [latex]\frac{12}{11}[/latex]
= 6:[latex]\frac{720}{11}[/latex], 6:00
Not Possible
Note: minute and hour hand does not make 180° angle between 5 to 6 and 6 to 7 O' clock.
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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[latex]\frac{3}{11}[/latex]
(b) 8: 36, 8:51[latex]\frac{3}{11}[/latex]
(c) 8:09, 8:47[latex]\frac{4}{11}[/latex]
(d) 8: 7, 8: 28[latex]\frac{9}{11}[/latex]
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Answer: (b) 8: 36, 8:51[latex]\frac{3}{11}[/latex]
Solution:
[latex]\frac{Angle}{6}[/latex]= minutes
By unique Formula
= H : [latex] \left ( H \times 5\pm \frac{Angle}{6} \right )\times \frac{12}{11}[/latex]
= 8: [latex] \left ( 8 \times 5\pm 7 \right )\times \frac{12}{11}[/latex]
= 8: [latex]\left ( 40\pm 7 \right )\times \frac{12}{11}[/latex]
= 8: [latex]\left ( 40\dotplus 7 \right )\times \frac{12}{11}[/latex], 8: [latex]\left ( 40 - 7 \right )\times \frac{12}{11}[/latex]
= 8:47 x [latex]\frac{12}{11}[/latex], 8 : 33 x [latex]\frac{12}{11}[/latex]
= 8:[latex]\frac{564}{11}[/latex], 8: [latex]\frac{396}{11}[/latex]
= 8:51[latex]\frac{3}{11}[/latex], 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[latex]\frac{9}{11}[/latex]minute loss
(b) 32[latex]\frac{8}{11}[/latex]minute gain
(c) 33[latex]\frac{9}{11}[/latex]minute gain
(d) 32[latex]\frac{8}{11}[/latex]minute loss
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Answer: (b) 32[latex]\frac{8}{11}[/latex]minute gain
Solution:
Normal watch overtakes in
= 65[latex]\frac{5}{11}[/latex] minute
This watch overtakes in = 64 minute
It means In 64 minutes the clock gains
=65[latex]\frac{5}{11}[/latex] - 64
= 1[latex]\frac{5}{11}[/latex] = [latex]\frac{16}{11}[/latex] min
“In one day = 24 × 60 minutes”
Then in 1 minute clock gains
= [latex]\frac{16}{11\times 64}[/latex]
In 24 × 60 Minute clock gains
=[latex]\frac{16\times 24\times 60 }{11\times 64}[/latex]
= [latex]\frac{360}{11}[/latex] minutes
= 32[latex]\frac{8}{11}[/latex] minutes
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