Question

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

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

Answer 1

The correct option is B

$21.81min$

The minute hand of a clock covers ${360}^0$ in $60min$ or $6^0$ in $1min.$

The hour hand of a clock covers ${360}^0$ in $12hrs$ or ${30}^0$ in $1hour$ or $0.5^0$ in $1min.$

At $4:00,$ the minute hand has covered $0^0$ and the hour hand has covered ${120}^0$.

Let the time after which the hands coincide be $xmin.$

So, the hour hand covers $120+\left(\frac{x}{2}\right)$up to that time and the minute hand covers $6x^0$ up to that time. When they coincide the angles should be the same.

So we can write $120+\left(\frac{x}{2}\right)=6x$

$$\begin{gathered} \Rightarrow \frac{\left(12x-x\right)}{2}=120 \\ \Rightarrow 11x=240 \\ \Rightarrow x=\frac{240}{11}min \\ =21.81min \end{gathered}$$

Hence, the correct option is B.