Question

A container is filled with 56 litres of pinapple juice. 8 litres of pinapple juice are extracted and the container is refilled with mango juice. The content of the container is thoroughly mixed and 8 litres of the mixture are then extracted and the container is again refilled with mango juice. What is the ratio of mango juice to pinapple juice in the final mixture?

Answer 1

If it's refilled with 8 litres of mango juice, the resulting mixture will be 8 parts mango and 48 parts pine, or 1 part mango, 6 parts pine. (AKA, roughly 16.67% mango juice).

Now, if they take out 8 litres from that mixture, that 8 litres will also be 1 part mango and 6 parts pine, leaving you with 48 litres of 1 part mango, 6 parts pine.

Hang on, because it gets tricky from here. We're going to use a formula here:

<---- where there are q[1] litres of p[1] % that we start with, and we add q[2] litres of p[2] % mix, and so we'll end up with a mixture that is (q[1] + q[2]) liters big that will have a different percent mixture p[3] from what we started.


We started with 48 liters that is 16.67% mango. So <---- change the percent to a decimal.

We're going to add 8 liters of pure mango juice, so <--- The 100% mango juice is the 1 in decimal.

As total mix, we'll have litres which is 48 + 8 = 56, BUT the percentage mango of the new mixture will surely be different.

So our equation so far is: . All we have to do is solve for .

<---- simplified

<--- roughly 28.57% mango juice or mango juice. Since mango is 2/7 of the mixture, the other 5/7 is pine. The problem asked for the ratio between mango to pine, and that would be the 2:5.