Discussion

Explanation:

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

⇒ 50° = |$\left|30\times 7-\frac{11}{2}\mathrm{m|}\right|$

Case 1:
⇒ 50° = 210 - $\frac{11}{2}$m

⇒ $\frac{11}{2}$m = 160°

⇒ m = $\frac{320}{11}$ = 29$\frac{1}{11}$minutes

∴ The hands will be at an angle of 50° at 7 : 29$\frac{1}{11}$.

Case 2:
⇒ -50° = 210 - $\frac{11}{2}$m

⇒ $\frac{11}{2}$m = 260°

⇒ m = $\frac{520}{11}$ = 47$\frac{3}{11}$minutes

∴ The hands will be at an angle of 50° at 7 : 47$\frac{3}{11}$.

Hence, option (d).

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