Question

A clock is set at $4:00$ am. It loses $16$ minutes in $24$ hours. What will be the correct time when the clock indicates $9:00$ pm on the $4$th day?

• A. $8:00$ pm
• B. $7:00$ pm
• C. $10:00$ pm
• D. $11:00$ pm

Answer 1

The correct option is C $10:00$ pm

Time from $4:00$ am on a day to $9:00$ pm on the $4$th day $=89$ hours
Since clock loses $16$ minutes in $24$ hours,
$\therefore$ $23$ hours $44$ minutes of this clock $=24$ hours of the correct clock
or, $\frac{356}{15}$ hours of this clock $=24$ hours of the correct clock
$\Rightarrow 1$ hour of this clock $=\frac{24\times 15}{356}$ hours of the correct clock
$\Rightarrow 89$ hours of this clock $=\frac{24\times 15\times 89}{356}$ hours of the correct clock
$\therefore 89$ hours of this clock $=90$ hours of the correct clock
Hence, the correct time is $10:00$ pm on $4$th day.