A clock is set right at $5$ a.m. The clock loses $16$ minutes in $24$ hours. What will be the right time when the clock indicates $10$ p.m on the 4th day?

The correct option is C $11$ p.m

In $24$ hours clock loses $=16$ minutes

In one hour clock loses $=\frac{16}{24}\times \frac{1}{60}=\frac{1}{90}hour$

Let the correct time be after $x$ hours

Time from $5$ am to $10$ pm on 4th day $24+24+24+17=89$ hours

$\therefore x-\frac{x}{90}=89$

$x=90$ hours

Therefore the correct time will be $11$ pm