At what time between 8 and 9 o'clock will the hands of a

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At what time between 8 and 9 o'clock will the hands of a clock be at right angle ?

1. 8 : 16³/₁₁
2. 8 : 27³/₁₁
3. 8 : 17³/₁₁
4. None of these

Correct Option: B

Consider exactly at 8 : 00, minute hand is at position '12' and hour hand is at '8' hence angle between these two hands at 8 : 00 is 240°.
Case (i) when minute hand is behind Hour hand then required time is (240 - 90)/(11/2) = 150/(11/2) = 300/11 = 27 3/11 minute
Case (ii) when minute hand is ahead of four hand then required time is (240 + 90)/(11/2) = 330/(11/2)
= 330 x 2/11 = 60 minute i.e., at 9 : 00 PM