Question

If `20` quarts of milk contains `2` quarts of butter fat, how much pure water would be need to be added to the milk to make it `4%` butter fat?

Answer 1

`color(red)(30)` quarts of pure water would need to be added.

Explanation:

Suppose that the required amount of water that would need to be added was `color(red)x` quarts.

The total resulting volume would be `color(blue)(20+color(red)x)`

The ratio of butter fat (given `color(green)2` quarts of butter fat) to total volume would be:
`color(white)("XXX")color(green)2/(color(blue)20+color(red)x)`

We are told that this ratio needs to be `color(magenta)(4%)`
and
Noting that `color(magenta)(4%)=color(magenta)(4/100)=color(magenta)(2/50)`

We have, as a requirement:
`color(white)("XXX")color(green)2/(color(blue)20+color(red)x)=color(magenta)(2/50)`

`rArr color(blue)(20+color(red)x)=color(green)50`

`rArr color(red)x= color(green)50-color(blue)20=color(red)30`