At what time between 9 o'clock and 10 o'clock, will the

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At what time between 9 o'clock and 10 o'clock, will the hands of a clock be in the same straight line but not together ?

1. 16²/₁₁ min past 9
2. 16²/₁₁ min past 10
3. 16⁴/₁₁ min past 9
4. 16⁴/₁₁ min past 10
5. None of the above

Correct Option: C

At 9 o'clock, the hour hand is at 9 and the minute hand is at 12. it means that the two hands are 15 min spaces apart .To be in the same straight line (but not together ), they will be 30 min space apart .
∴ The minute hand will have to gain (30 - 15) = 15 min space over the hour hand .

As we Know, 55 min spaces are gained in 60 min.
∴ 15 min will be gained in (60/55 x 15) min = 180/11 = 16⁴/₁₁ min

Hence, the hands will be in the same straight line but not together at 16⁴/ ₁₁ min past 9.