Discussion

Explanation:

The faulty clock gains 5 seconds every 3 minutes.
⇒ Faculty clock covers 185 seconds for every 180 seconds covered by actual clock

⇒ $\frac{\mathrm{Time} \mathrm{covered} \mathrm{by} \mathrm{faulty} \mathrm{clock}}{\mathrm{Actual} \mathrm{time} \mathrm{covered}}$ = $\frac{185}{180}$ = $\frac{37}{36}$

From 7 a.m. till quarter past 4 p.m., the faulty clock covers 9$\frac{1}{4}$ = $\frac{37}{4}$ hours

⇒ $\frac{\mathrm{Time} \mathrm{covered} \mathrm{by} \mathrm{faulty} \mathrm{clock}}{\mathrm{Actual} \mathrm{time} \mathrm{covered}}$ = $\frac{37}{36}$

⇒ $\frac{{\displaystyle \raisebox{1ex}{$37$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}}{\mathrm{Actual} \mathrm{time} \mathrm{covered}}$ = $\frac{37}{36}$

⇒ Actual time covered = 9 hours.

∴ Actual time is 9 hours after 7 am. i.e., 4 p.m.

Hence, option (b)

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