At present, an accurate clock shows 16:20 hrs. By how many degrees will the hour hand rotate when the clock shows the mirror image of the present time? (Assume the mirror is kept along the vertical plane.)
100°
The hour hand turns 360° in 12 hours, that is 30° per hour or 0.5° per minute. The reflection of a time in a vertical mirror is found by subtracting the time from 11:60 (that is, 12:00).
Step 1 — 16:20 hrs is 4:20 on the dial.
Step 2 — Mirror image of 4:20 = \(11{:}60 - 4{:}20 = 7{:}40\).
Step 3 — Time taken by the hour hand to move from 4:20 to 7:40 = 3 hours 20 minutes = 200 minutes.
Step 4 — Angle turned = \(200 \times 0.5^\circ = 100^\circ\).
A turn of 180° would need 6 hours, 210° would need 7 hours and 215° would need 7 hours 10 minutes; none of these matches the 3 hours 20 minutes between the actual time and its reflection.
100° option is correct.
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