At what time between 3:30 and 4 will hands of a clock be at the right angles?

At 3 o’clock the hands are at 15 minutes spaces apart. To be at the right angles and that too between 3:30 and 4, the minute hand has to gain (15 +15) = 30 minutes = 60/55×30 = 32*8/11 minutes ∴ Required time = 32*8/11 minutes past 3.

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