Question

What will be the measurement of the angle made by the hour and minute hands of a clock when the time is ‘quarter past 3’?

• A. 6°
• B. 7$\frac{1}{2}$°
• C. 7$\frac{3}{4}$°
• D. 8°

Hint:

Use $\theta = |30H - \frac{11}{2}M|$ to find the angle between hour and minute hands quickly.

Answer 1

The Correct Option is B

The angle between the hour and minute hands at time $H:M$ is given by the formula: \[ \theta = \left|30H - \frac{11}{2} M\right|. \] For quarter past 3, $H=3$ and $M=15$. The calculation is: \[ \theta = |30 \times 3 - \frac{11}{2} \times 15| = |90 - 82.5| = 7.5^\circ. \] Consequently, the angle between the hands is $7\frac{1}{2}^\circ$ (7.5 degrees). *Note:* Option (c) 7$\frac{3}{4}^\circ$ (7.75°) is incorrect.