Discussion

Explanation:

The faulty clock gains 10 minutes every 24 hours.
⇒ The faulty clock gains 5 minutes every 12 hours.
⇒ Faculty clock covers 725 minutes for every 720 minutes covered by actual clock

⇒ $\frac{\mathrm{Time} \mathrm{covered} \mathrm{by} \mathrm{faulty} \mathrm{clock}}{\mathrm{Actual} \mathrm{time} \mathrm{covered}}$ = $\frac{725}{720}$ = $\frac{145}{144}$

From 6 a.m. till 2 p.m. next day, the faulty clock covers 20 hours

⇒ $\frac{\mathrm{Time} \mathrm{covered} \mathrm{by} \mathrm{faulty} \mathrm{clock}}{\mathrm{Actual} \mathrm{time} \mathrm{covered}}$ = $\frac{145}{144}$

⇒ $\frac{{\displaystyle 32}}{\mathrm{Actual} \mathrm{time} \mathrm{covered}}$ = $\frac{145}{144}$

⇒ Actual time covered = $32\times \frac{144}{145}$ = 31 hours 47 minutes.

∴ Actual time is 31 hours and 47 minutes after 6 am. i.e., 1:47 p.m.

Hence, option (d).

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