Question

At what time between 3pm to 4PM the angle between the minute and hour hands ahead be 9°, the minute hand being ahead of the hand ? (A) 3h 15m 45s (B) 3 h 16 m 00s (C) 3h 16m 30s (D) 3h 18m 00s​

Answer 1

Answer:

C)3h 16m 30s

Step-by-step explanation:

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Answer 2

Given,

Time period 3 pm to 4 pm.

To find,

Time at which angle between the hour hand and the minute hand is 9°.

Solution,

In the clock, the minute hand covers a complete angle of 360° every hour.

We can calculate the angle it covers for every minute, and it comes out to be,

 = 360/60 = 6° per minute.

Similarly, we can find for the hour hand. Hour hand makes a complete rotation in 12 hours which is 720 minutes.

Angle covered in each minute = 360/720 = 0.5° per minute.

At 3 pm, the minute hand will be at 12. Let us assume that position to be 0°.

Then hour hand will be at 0.5°*3*60 = 90°

Let us assume that after time t, the minute hand and hour hand has a difference of 9°.

Hour hand after time t = 90° + 0.5°*t

Minute hand after time t = 6°*t

According to the question,

6°*t - (90° + 0.5°*t) = 9°

5.5°*t = 99°

t = 18 minutes.

Therefore, the angle between the minute hand and hour hand with hour hand being ahead will be 9° at 3 h 18 m 00s.