A clock is set right at 5 A.M. The clock loses 16 minutes in 24 hours. What will be the true time when the clock indicates 10 P.M. on 4^th day?

The logic follows here is:

Number of hours between 5 A.M. to 10 P.M. of the Fourth day = 24 + 24 + 24 + 17 = 89 hours

The clock loses 16 minutes in 24 hours.

Thus, the clock shows 23 hours 44 minutes = Actual correct clock time is 24 hours.

→ 23 + 44/60 = 24 hours

→ 23 + 11/15 = 24 hours

→ {(23 × 15) + 11}/15 = 24 hours

→ 356/15 = 24 hours

Now, for 1 hour = (24 × 15) / 356

→ 360 / 356

And, for 89 hours = 89 × 360 / 356

→ 90 hours

Therefore, the true time of the clock is (90 - 89 = 1 hour) more than the current showing time = 10 P.M. on the fourth day + 1 hour = 11 P.M. on the fourth day.

Hence, the correct answer is "11 P.M.".