Question

Ben fills a glass with orange juice and lemonade in the ratio 1:4 by volume.
He mixes the liquid that is in the glass.
Ben drinks 1/4
of this liquid.

He then fills the glass using orange juice.
Work out the ratio of orange juice to lemonade, by volume, that is now in the glass.
Give
your ratio in its simplest form.

Answer 1

O = Orange, L = Lemonade

1/4 O + 3/4 L = x

Drink 1/4 of x, ratio of O and L doesn't change

1/4 O + 3/4 L = 3x/4

Fill up by adding 1/4 O

So it becomes 1/4 O + 1/4 O + 3/4 L = x

1/2 O + 3/4 L = x

Ratio of O to L = 1/2 divided by 3/4

= 1/2 * 4/3

Ratio of orange to Lemonade is 2:3