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# At what time between 5.30 and 6 will the hands of a clock be at right angles?

Option :

Explanation:

Solution:
At 5 o'clock, the hands are 25 min. spaces apart.
To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.
55 min. spaces are gained in 60 min.
40 min. spaces are gained in
$\begin{array}{rl}& \left(\frac{60}{55}×40\right)\phantom{\rule{thinmathspace}{0ex}}min=43\frac{7}{11}\phantom{\rule{thinmathspace}{0ex}}min\\ & \therefore \text{Required}\phantom{\rule{thinmathspace}{0ex}}\text{time}=43\frac{7}{11}\phantom{\rule{thinmathspace}{0ex}}min.\phantom{\rule{thinmathspace}{0ex}}past\phantom{\rule{thinmathspace}{0ex}}5\end{array}$