# If the angle between the hand of clock be 54 degree and the time it reads between 7 and 8. Find the time?

Hi,
Formula for angles between two hands of a clock
there are 2 possibilities
ø = angle, h = number of hours completed. and m = number of minutes.
ø = 30h – 11/2 m ----------when minute hand is in first 1/2 (between 12 to 6)
54 = 30 × 7 – 11/2 m
11/2 m = 156
m = 28.36 min = 28 4/11 min = 21.8 s.
at 7 hr 28 4/11 min

for other possibility
ø = 11/2 m – 30h ----------when minute hand is in second 1/2 (between 6 to 12)
54 = 11/2 m – 30 × 7
11/2 m = 264
m = 48 min
at 7 hr 48 min
Regards

• -3
Let the hour hand= x minutes past seven or hour hand= 35+x minutes away from 12 Then minute hand = 12x minutes away from 12 The speed ratio of minute hand and hour hand hand is 12 Separation between hour hand and minute hand = 35+x−12x =35−11x In the 360degree angle there are 60 minutes of clock Hence each minute of clock =360/60=6 degree angle Hence separation between hour hand and minute hand in degrees= (35−11x)×6 degrees Hence (35−11x)×6 =54 210 −66x=54 or 66x=210−54=156 or x= 156/66= 2.37 Position of minute hand = 2x=12×2.37=28.37 Hence time is 28.37 minutes past 7'O clock i.e 28 minues and 22.2 seconds past 7'O clock
• 1
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