Arun's Time Table

Sleeping: One third of a day
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Playing: One eight of a day
Studying: $\frac{1}{4}$ of a day
How many hours does Arun take for

Sleeping?  hours

Studying?    hours

Playing?  hours
What part of the day does he use for other activities?

 
Total number of hours in 1 day = 24
Arun sleeps one-third of a day.
Number of hours that Arun sleeps = 24 $÷$ 3
                                                        = 8 

Thus, Arun sleeps for 8 hours in a day.
Arun plays for one-eighth of a day.
Number of hours Arun takes to play = 24 $÷$ 8
                                                           = 3
Arun studies one-fourth of a day.
Number of hours Arun takes to study = 24 $÷$ 4
                                                             = 6

Total number of hours spent in studying, playing and sleeping = 6 + 3 + 8
                                                                                                    = 17
Number of hours left for other activities = 24 − 17
                                                                  = 7
So, part of the day used for other activities = $\frac{7}{24}$

Thus, Arun uses seven twenty-fourth of the day for other activities.