Discussion

Explanation:

The faulty clock gains 1 minute every 60 minutes.
⇒ Faculty clock covers 61 minutes for every 60 minutes covered by actual clock

⇒ $\frac{\mathrm{Time} \mathrm{covered} \mathrm{by} \mathrm{faulty} \mathrm{clock}}{\mathrm{Actual} \mathrm{time} \mathrm{covered}}$ = $\frac{61}{60}$

From 1 p.m. till 6 p.m., the faulty clock covers 5 hours

⇒ $\frac{\mathrm{Time} \mathrm{covered} \mathrm{by} \mathrm{faulty} \mathrm{clock}}{\mathrm{Actual} \mathrm{time} \mathrm{covered}}$ = $\frac{61}{60}$

⇒ $\frac{{\displaystyle 5}}{\mathrm{Actual} \mathrm{time} \mathrm{covered}}$ = $\frac{61}{60}$

⇒ Actual time covered = $\frac{300}{61}$ = 4 hours 55$\frac{5}{61}$ minutes.

∴ Actual time is 4 hours 55$\frac{5}{61}$ minutes after 1 p.m. i.e., 5 : 55$\frac{5}{61}$ p.m.

Hence, option (b)

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