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A clock was set at right time at 12:00 noon. It loses 10 minutes every hour. What is the difference in angle made by minute hand and hour hand at 6:30 pm and angles made by minute hand and hour hand at actual time? Note: Consider acute angle.

A clock was set at right time at 12:00 noon. It loses 10 minutes every hour. What is the difference in angle made by minute hand and hour hand at 6:30 pm and angles made by minute hand and hour hand at actual time? Note: Consider acute angle. Correct Answer 2.5°

Angle covered by hour hand in one hour i.e. 60 minutes is 360°/12 = 30°.

At 6:30 pm, the minute hand will be at 6 and hour hand will be in between 6 and 7. Hence, the angle between minute hand and hour hand at 6:30 pm will be 30° × 30/60 = 15°.

Time loss till 6:30 pm will be 10 minutes × 6½ hours = 65 minutes.

Therefore, the actual time will be 6:30 pm + 65 minutes = 7:35 pm.

At 7:35 pm, the minute hand will be at 7and hour hand will be in between 6 and 7. Hence, the angle between minute hand and hour hand at 7:35 pm will be 30° × 35/60 = 17.5°.

The difference in angle made by minute hand and hour hand at 6:30 pm and angles made by minute hand and hour hand at actual time i.e. 7:35 pm is (17.5° - 15°) = 2.5°.

Hence, 2.5° is the correct answer.

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