Discussion
Given below are two statements:
Statement I : An accurate clock shows the time as 3:00 pm. After the hour hand has moved 135°, the time would be 7:30 pm.
Statement II : The angle between the minute hand and hour hand when the clock shows 4:25 pm. is 17.5°.
In the light of the above statements, choose the correct answer from the options given below:
Answer: A
Both Statement I and Statement II are true.
The hour hand moves 30° per hour, so 135° is \(135 / 30 = 4.5\) hours. From 3:00 pm that is 7:30 pm. Statement I is true.
For Statement II use the clock-angle formula \(|30H - 5.5M|\):
\[ |30 \times 4 - 5.5 \times 25| = |120 - 137.5| = 17.5^\circ \]
Statement II is true. The trap is to forget that the hour hand moves on from the 4 during the 25 minutes (by 12.5°).
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