CUET UG 2025 — General Test Logical Reasoning

The minute hand at 30 minutes points at the 6 on the clock.

The minute hand position from 12 o'clock:

$$\text{Minute hand angle} = 30 \times 6°$$Minute hand angle=30×6°

$$\text{Minute hand angle} = 180°$$Minute hand angle=180°

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The hour hand at 8:30 is past the 8 and has moved partway toward the 9.

At 8:00, the hour hand position from 12 o'clock:

$$\text{Hour hand angle at 8:00} = 8 \times 30°$$Hour hand angle at 8:00=8×30°

$$\text{Hour hand angle at 8:00} = 240°$$Hour hand angle at 8:00=240°

In 30 minutes, the hour hand moves:

$$\text{Additional movement} = 30 \times \dfrac{30°}{60}$$Additional movement=30×6030°​

$$\text{Additional movement} = 15°$$Additional movement=15°

Total hour hand position at 8:30:

$$\text{Hour hand angle} = 240° + 15°$$Hour hand angle=240°+15°

$$\text{Hour hand angle} = 255°$$Hour hand angle=255°

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The angle between the hands:

$$\text{Angle} = |255° - 180°|$$Angle=∣255°−180°∣

$$\text{Angle} = 75°$$Angle=75°

Therefore, the angle between the clock hands at 8:30 is $75°$75°.