Discussion

Explanation:

Hands overlap when the angle between the two hands is 0°.

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

⇒ 0° = |$\left|30\times 3-\frac{11}{2}\mathrm{m|}\right|$

⇒ 0° = 90 - $\frac{11}{2}$m

⇒ m = $\frac{180}{11}$ = 16$\frac{4}{11}$minutes

∴ The hands will coincide at 3 : 16$\frac{4}{11}$.

Hence, option (d).

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