Question

At what time between 6 a.m. and 7 a.m. will the minute hand and hour hand of a clock make an angle closest to ${60}^{\circ }$

• A. 6:22 a.m
• B. 6:27 a.m
• C. 6:38 a.m
• D. 6:45 a.m

Answer 1

The correct option is A 6:22 a.m

Any angle and corresponding time can be driven by

$[5x-\left(\frac{D^0}{6}\right)]\times \frac{12}{11}$

Between 6 and 7 a.m angle have to be ${60}^{\circ }$

Put $x=6andD={60}^{\circ }$

$[5\times 6-\frac{{60}^{\circ }}{6}]\times \frac{12}{11}=20\times \frac{12}{11}=21\frac{9}{11}$

$Soat4:21\frac{9}{11}anglebetweenminutesandhourhandwillbe{60}^{\circ }$

In given question angle have to close to ${60}^{\circ }$ nearest option is 6 : 22.