Question

The angle between the hour hand and the minute hand of a clock when time is 3 : 25 will be
1. 47 \(\frac{1}{2}\)°
2. 42 ​\(\frac{1}{2} \)° ​
3. 60°
4. 45°

Answer 1

Correct Answer - Option 1 : 47 \(\frac{1}{2}\)°

Given Time: 3 : 25

Formula:

|(60H – 11M ) /  2|

Angle at 3 : 25

|(60 × 3 – 11 × 25) / 2|

|180 – 275 / 2| = 95 / 2 = 47 \(\frac{1}{2}\)°

TRICK:

Hour hand → 1 hour = 30°

3 hour → 90°

1 minute = 1/2°

25 minute = 12.5°

Minute hand → 1 minute = 6°

25 minute = 150°

Now, Angle made by the hour hand – Angle made by the minute hand

Required Angle = |90° + 12.5° – 150°| = |102.5° – 150°| = 47 \(\frac{1}{2}\)°

Hence, 47 \(\frac{1}{2}\)° is correct.