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A minute hand of a clock loses 30° every hour. The clock was set at 11:00 am. The acute angle made by minute hand and hour hand at actual time when the clock shows 4:00 pm.

A minute hand of a clock loses 30° every hour. The clock was set at 11:00 am. The acute angle made by minute hand and hour hand at actual time when the clock shows 4:00 pm. Correct Answer 17½°

Every hour minute hand covers 360°. Therefore in 30°, the minute hand covers 5 minutes. That means the minute hand loses 5 minutes every hour.

From 11:00 am to 04:00 pm, there is 5 hours and hence, the minute hand will lose 5 × 5 = 25 minutes.

Therefore, the actual time will be 04:25 pm.

In one hour i.e. 60 minutes, the hour hand covers 30°. Therefore in 25 minutes, the hour hand will cover 25 × 30°/60 = 12½°.

AT 04:25 pm, the minute hand will be at 5 and hour hand will be somewhere in between 4 and 5.

Hence, acute angle between minute hand and hour hand at 04:25 pm will be (30° - 12½°) = 17½°.

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