Question

At what time between $1.30pm$ and $2pm$ will both the hands of a clock be at right angles?

• A. $4\frac{6}{11}$
• B. $61\frac{5}{11}$
• C. $\mathrm{Both}\left(A\right)\&\left(B\right)$
• D. None of these

Answer 1

The correct option is A $4\frac{6}{11}$

The angle between $2$ successive numbers in the clock is $\frac{360}{12}={30}^{\circ }$

The angle between successive dots is $\frac{360}{60}=6^{\circ }$

For one rotation of minutes hand hours hand rotates by ${30}^{\circ }$

$⟹$ For increase in $1$ minute there is increase of ${\frac{1}{2}}^{\circ }$ for hours hand

At $1.50\text{pm}$

Angle Between hands of clock at $90+\frac{50}{2}=115$

For every $1$ min there is a decrease of ${\frac{11}{2}}^{\circ }$

For every $x$ min there is a decrease of ${25}^{\circ }$

$⟹x=\frac{25\times 2}{11}=4\frac{6}{11}$min

So at $4\frac{6}{11}$ pm the hands are perpendicular to each other.