Question

a jug is filled with 2l and 4l of orange juice such that the two liquids are completely mixed.what percentage of the mixture must be removed and replaced with water to create a mixture with a water to orange juice ratio of 2:1?​

Answer 1

Answer:

50% of the mixture must be removed

Answer 2

Given,

A jug filled with 2lt water and 4lt orange juice.

To find,

Percentage of the mixture that must be removed and replaced with water to create a mixture with water to orange juice ratio of 2:1

Solution,

The mixture present in the jug contains 6lt of liquid which is a mixture of water and orange.

Let us assume we remove $a$ litres of the mixture.

Amount of liquid left = 6 -  $a$ litres.

Water left in the jug = $(6 - a)* \frac{1}{3} = \frac{(6 - a)lt}{3}$

Orange juice left in the jug = $4 - \frac{2}{3}a = \frac{(12- 2a)lt}{3}$

Now, the amount of mixture removed was replaced by water. Therefore, total water in jug = $\frac{(6 - a)lt}{3} + a = \frac{(6 +2a)lt}{3}$

According to the question,

Water/ Juice = $\frac{1}{2}$

$\frac{6 + 2a}{ 12 - 2a} = 2/1\\\\6 +2a = 24 - 4a\\6a = 18\\a = 3$

Percentage = $\frac{3}{6}*100% = 50%$% = 50%

Therefore, 50% of the mixture must be removed and replaced with water to create water to orange juice ratio of 2:1.