At 9 'o clock, the Minute Hand is ahead of Hour Hand by 45 minutes. The hands will be opposite to each other when there is a space of 30 minutes between them. This will happen when the Minute Hand gains 15 minutes space over Hour Hand. Time taken by Minutes Hand to gain 15 minutes =15×(1+
1
11
)=15+
15
11
=15+1
4
11
=16
4
11
minutes. Hence the Hands are opposite to each other at 16