Question

During 24 hours a radio station spends 1/5 of the time playing rock music,2/3 playing hip hop, and the rest playing dance music.How much time is spent playing dance music?

Answer 1

`3.2\:\text{hours}` is spent playing dance music.

Explanation:

Given: During
`24` hours a radio station spends
`(1)/(5)` of the time playing rock music,
`(2)/(3)` playing hip hop, and the rest playing dance music.

To find: How much time is spent playing dance music?

Solution:

We have,

Radio station spends
`(1)/(5)` of the time playing rock music.

Radio station spends
`(2)/(3)` of the time playing hip hop.

Radio station spends rest of the time playing dance music.

So,

Time spend on playing rock music
`=(1)/(5)*24 = 4.8\:\text {hours}`

Time spend on playing hip hop
`=(2)/(3)*24 = 16\:\text {hours}`

Now, total time radio station spends on all the three music is
`24` hours.

Therefore, rest of the time
`=24-(16+4.8)=3.2\:\text{hours}`

It is given that in the rest of the time, the radio station plays dance music.

Hence,
`3.2\:\text{hours}` is spent playing dance music.