Question

At how many points between 10 o'clock a nd 11 o'clock are the m inute hand and hour h and of a clock at an an gle of 30 degrees to each other?

Answer 1

At the time of 10′o clock ,hours hand 300° ahead of minutes hand and in one minutes time minutes hand covers (11/2)° more than hours hand .. already hours hand 300° ahead of minutes hand…if minutes hand travels 270° more than hours hand ,then angle between hours and minutes hand is 30°….for that time taken is (270/(11/2)°)=540/11=49(1/11)min,so at the time of 10:49(1/11) min angle is 30°

Or

Angle=mod((11/2)m~30h)

30°=mod((11/2)m~300)

330°=(11/2)m,270=(11/2)m

m=60,49(1/11)

11:00,10:49(1/11)

In b/w 10′o clock and 11′o clock at 10:49(1/11)m hands of the clock are 30° apart

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   hope this helps