A clock is set right at 7AM on 12th January, 2022. The clock loses 18 minutes in every 24 hours. What will be the approximate true time when clock indicates 7PM on 17th January 2022?

Let $$'x'$$ be the true time when the clock indicates 7 PM on 17th January 2022.

Let $$'y'$$ be the number of hours elapsed between 7 AM on 12th January, 2022 and $$'x'$$

The clock loses 18 minutes per 24 hours. 

For one hour, it loses$$=\frac{18}{24\ \times \ 60}=\frac{1}{80}\ \ hrs$$

For $$'y'$$ hours it loses = $$\frac{y}{80}\ \ hrs$$

Hence, the number of hours elapsed between 7 AM on 12th January 2022 and 7 PM on 17th January 2022 = $$y-\frac{y}{80}$$

$$y-\frac{y}{80}=5\times\ 24+12$$

$$\frac{79y}{80}=132$$

$$y=133.671\ hrs$$

$$y=24\times\ 5.5+1.67\ hrs$$

Hence, the approximate true time when the clock indicates 7 PM on 17th January 2022 = 7 AM, 12th January 2022 + $$'y' hrs$$

= 7 AM, 12th January 2022 + 5days +12 hrs +1.67 hrs

= 7 PM on 17th January 2022 + 1.67 hrs

= 08:40:15 PM 17th January 2022.

Option (D) is the answer.