A clock is set at 4am. It loses 16 minutes in 24 hours. What will be the correct time when the clock indicates 9pm on the 4th day?

10:00 PM

Time from 4am on first day to 9pm on the 4th day = 89 hours

As per the question, 23 hrs 44 minutes of this clock = 24 hours of the correct clock as this clock loses 16 minutes in 24 hours.

Here,

23 hrs 44 minutes = 23 + \(\frac{44}{60}\) hrs = 23 + \(\frac{11}{15}\) hrs = \(\frac{356}{15}\) hrs

Hence,

⇒ \(\frac{356}{15}\) Hrs of this clock = 24 hours of correct clock

⇒ 1 Hr of this clock = 24 × \(\frac{15}{356}\) hours of correct clock

⇒ 89 hours of this clock = 24 × \(\frac{15}{356}\) × 89 = 90 hours of the correct clock,

it means,  the correct clock gains one hour over the incorrect clock.

Therefore, the correct time on the fourth day would be 9 + 1 = 10pm.