Find the exact time when the angle between hour-hand and the minute-hand of a clock will be : (i) 440 for the first time after 12 O’clock. (ii) 590 for the first time after 6 O’clock
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Answer:
12 : 08
6 : 22
Step-by-step explanation:
Angle 44° after 12 O' Clock for 1st time between hour-hand and the minute-hand
A minute Hand moves 360° in 1 hr
=> 6° Every 1 min
& Hour Hand move 30° in 1 hr
=> 0.5° Every 1 Min
Angle between Hr hand & Minute hand in 1 minute
= 6 - 0.5
= 5.5°
so 44° angle will be in 44/5.5 = 8 Mins
Time Would be 12 : 08
Angle 59° after 6 O' Clock for 1st time between hour-hand and the minute-hand
Initially angle = 180° to get angle 59°
=> 180° - 59° = 121° movement required between hr hand & minute hand
Let say T minutes are Taken
= 121/5.5
= 22
Time Would be 6 : 22
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