Question

Tim is a sports fan. He spends the "TV-time" of his holidays watching football, cricket, golf, MotoGP, Formula1 races, tennis, badminton and hockey games. If he spends two-fifths of his TV-time watching the first four sports and devotes what's left of his TV-time equally to each of the other sports, what fraction of his TV-time does he spend watching badminton?

Answer 1

Tim spends
`(3)/(20)` of his TV time watching badminton.

Explanation:

Step 1:

Tim watches a total of 8 sports. He spends
`(2)/(5)` of his TV time watching the first four.

So first we need to calculate how much TV time is left to watch the remaining sports.

The TV time left to watch the other sports
`= 1 - (2)/(5) = (5-2)/(5) = (3)/(5)`.

So
`(3)/(5)` of his TV time is spent equally on the other 4 sports.

Step 2:

As there are 4 sports remaining, he spends the
`(3)/(5)` of his time on all four sports equally. We need to determine what that time is.

The time spent on the remaining four sports
`((3)/(5))/(4) = ((3)/(5))((1)/(4) ) = (3)/(20)`.

So Tim spends
`(3)/(20)` of his total TV time each on watching formula1 races, tennis, badminton and hockey games. So he spends
`(3)/(20)` of his TV time watching badminton.