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

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  $\frac{60}{55}\times 40$ min