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My question is- If the angle between the hour hand and the minute hand at $8$ hours and $x (>0)$ minutes is exactly $120^\circ$ then $(11x - 200)$ equals?

My solution is: $40$

I would like to know whether my solution is right and if not how to solve this question? Thank you!

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I would call "40" an answer rather than a solution. A solution would indicate how you came to the conclusion that 40 is the answer. – Jonas Meyer Jul 15 '12 at 7:11
well yes you are 40 the right answer? – mgh Jul 15 '12 at 7:13
yes I think you are correct. – Saurabh Jul 15 '12 at 7:18

The hour angle is $\theta_h = 240^{\circ}+\frac{m}{2}$ and the minute angle is $\theta_m = 6^{\circ} m$, where $m$ is the number of minutes past $8$ o'clock. Then the solution is given by $\theta_m+120^{\circ} = \theta_h$, which easily gives $m = \frac{240}{11}$. Your 'solution' follows from this.

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