Question

An alcohol addict drank 1/3 of the bottle and added water to fill the bottle completely. he drank 2/3 of the contents and again filled the bottle with water. what is the ratio of water to alcohol in the bottle now?

Answer 1

2:1 is the ratio of water to alcohol

Answer 2

Answer:

Alcohol : Water = 2 : 7

Step-by-step explanation:

We are given that the addict drank $\frac{1}{3}$ of the bottle.

So, the amount of alcohol left = $1-\frac{1}{3}$ = $\frac{2}{3}$.

Also, he added $\frac{1}{3}$ of water in the bottle.

So, the amount of water left = $\frac{1}{3}$.

Further, we have that,

He drank $\frac{2}{3}$ of the contents.

So, the amount of alcohol left = $(\frac{2}{3})(1-\frac{2}{3})$ = $\frac{2}{3}\times \frac{1}{3}$ = $\frac{2}{9}$

Also, So, the amount of water left = $(\frac{1}{3})(1-\frac{2}{3})$ = $\frac{1}{3}\times \frac{1}{3}$.

Finally, he also added the $\frac{2}{3}$ of the water.

So, the final amount of water in the bottle = $\frac{1}{3}\times \frac{1}{3}+\frac{2}{3}$ = $\frac{7}{9}$

Thus, the ratio of alcohol and water in the bottle is given by,

Alcohol : Water = $\frac{2}{9}$ : $\frac{7}{9}$

i.e. Alcohol : Water = 2 : 7