Question
At what time between 5:00 and 6:00 will the hands of clock be at right angles?

Answer

At 5 O'clock, the hour hand is at 5 and the minute hand is at 12 . It means the angle between the two hands of the clock is $150^{\circ}$. The hands of the clock will be at right angles twice between 5:00 and 6:00
For the first time: The minute hand had to cover a relative distance of $60^{\circ}$.
So the time required $=\frac{60}{5.5}$ minutes $=\frac{60 \times 2}{11}$ minutes $=10 \frac{10}{11}$ minutes
$=10 \mathrm{~min} 55 \mathrm{sec}$
Hence, the hands of the clock are at right angles at 5:10:55
For the second time: The minute hand had to cover a relative distance of $240^{\circ}$.
So the time required $=\frac{240}{5.5}$ minutes $=\frac{240 \times 2}{11}$ minutes $=43 \frac{7}{11}$ minutes
$=43 \mathrm{~min} 38 \mathrm{sec}$
Hence, the hands of the clock are at right angles at 5:43:38.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free