At what point of time after 3 O' clock, hour hand and minute

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At what point of time after 3 O' clock, hour hand and minute hand are at right angles for the first time ?

1. 9 O' Clock
2. 4 H 37¹/₆ min
3. 3 H 30⁸/₁₁ min
4. 3 H 32⁸/₁₁ min

Correct Option: D

Clock will make right angle at (5n + 15) x 12/11 min past n.
Given that, n = 3
∴ Clock will make right angle at ( 5 x 3 + 15 ) x 12/11 min past 3 . =30 x 12 / 11 min past 3.
= 32⁸/₁₁ min
So required time = 3 H 32⁸/₁₁ min