Question

At what time between 4 and 5, will the hands of a clock coincide?

• A. 15.81 min
• B. 21.81min
• C. 23.81 min
• D. 33.48 min

Answer 1

The correct option is B 21.81min

We know minute hand of a clock covers ${360}^{\circ }$ in $60min$ or $6^{\circ }$ in $1$ minute and hour hand of a clock covers ${360}^{\circ }$ in $12hrs$ or ${30}^{\circ }$ in $1$ hour or $.5$ degree in $1$ min.

So at $4:00$ the minute hand has covered $0$ degrees and hour hand has covered $120$ degrees

Now let time after which these two coincide be $x$ min.

So hour hand covers $120+\frac{x}{2}$ upto that time and minute hand covers $6x$ degrees upto that time when they coincide the angles should be same

So, $120+\frac{x}{2}=6x$

Solving we get $6x-\frac{x}{2}=120$

$\Rightarrow \frac{12x-x}{2}=120$

$\Rightarrow 11x=240$

$\Rightarrow x=\frac{240}{11}$minutes

$\therefore x=21.81mins$