Discussion

Explanation:

We know, angle between the hands of a clock (θ°) = |$\left|30\mathrm{h}-\frac{11}{2}\mathrm{m|}\right|$

⇒ 69° = |$\left|30\times 10-\frac{11}{2}\mathrm{m|}\right|$

Case 1:
⇒ 69° = 300 - $\frac{11}{2}$m

⇒ $\frac{11}{2}$m = 231°

⇒ m = 42 minutes

∴ The hands will be at an angle of 69° at 10 : 42.

Case 2:
⇒ -69° = 300 - $\frac{11}{2}$m

⇒ $\frac{11}{2}$m = 369°

⇒ m = $\frac{738}{11}$ = 67$\frac{1}{11}$minutes

∴ The hands will be at an angle of 69° at 10 : 67$\frac{1}{11}$.

Hence, option (b).

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