A container is initially $\frac{2}{5}$ full of fruit juice. 700 ml of water is added, and the container becomes $\frac{3}{4}$ full. We need to find: (i) the fraction of the container's capacity that corresponds to the added water. (ii) the fraction of the container's capacity that is separated if $\frac{4}{5}$ of the fruit drink is separated out. (iii) the amount of drink in one glass, if the separated amount is poured into 6 glasses equally. (iv) the amount of fruit drink remaining in the container.

1. Problem Description

A container is initially $\frac{2}{5}$ full of fruit juice. 700 ml of water is added, and the container becomes $\frac{3}{4}$ full. We need to find:

(i) the fraction of the container's capacity that corresponds to the added water.

(ii) the fraction of the container's capacity that is separated if $\frac{4}{5}$ of the fruit drink is separated out.

(iii) the amount of drink in one glass, if the separated amount is poured into 6 glasses equally.

(iv) the amount of fruit drink remaining in the container.

2. Solution Steps

(i) Let the capacity of the container be $C$. Initially, the container has $\frac{2}{5}C$ of fruit juice. After adding 700 ml of water, the container is $\frac{3}{4}$ full. Therefore,

$$\frac{2}{5}C + 700 = \frac{3}{4}C$$

$$\frac{3}{4}C - \frac{2}{5}C = 700$$

$$\frac{15 - 8}{20}C = 700$$

$$\frac{7}{20}C = 700$$

$$C = \frac{20}{7} \times 700 = 20 \times 100 = 2000 \text{ ml}$$

The capacity of the container is 2000 ml.

The fraction of the container's capacity that corresponds to the 700 ml of water is:

$$\frac{700}{2000} = \frac{7}{20}$$

(ii) The initial amount of fruit juice is $\frac{2}{5}C = \frac{2}{5} \times 2000 = 800$ ml.

If $\frac{4}{5}$ of the fruit drink is separated, the amount separated is $\frac{4}{5} \times 800 = 640$ ml.

The fraction of the container's capacity that the separated amount represents is:

$$\frac{640}{2000} = \frac{64}{200} = \frac{32}{100} = \frac{8}{25}$$

(iii) The separated amount of drink is 640 ml. This is poured into 6 glasses equally. The amount of drink in one glass is:

$$\frac{640}{6} = \frac{320}{3} = 106\frac{2}{3} \text{ ml}$$

(iv) The initial amount of fruit juice is 800 ml. The amount separated is 640 ml. The amount of fruit drink remaining is:

$$800 - 640 = 160 \text{ ml}$$

3. Final Answer

(i) The fraction of the capacity of the container that is the amount of water that was added is $\frac{7}{20}$.

(ii) The fraction of the capacity of the container that is the separated amount of drink is $\frac{8}{25}$.

(iii) The amount of drink in one glass is $\frac{320}{3}$ ml or $106\frac{2}{3}$ ml.

(iv) The amount of fruit drink remaining in the container is 160 ml.