Question

A glass contains alcohol and water in the ratio 1:4. A second glass contains the same
quantity of liquid, but this time the ratio of alcohol to water is 2:3: Each glass is
emptied into a third glass. What is the ratio of alcohol to water in the final mixture?

Answer 1

Ratio of alcohol to water in the first glass = 1:4

This can be written in a fraction as :-

$\color{hotpink}= \frac{1}{4}$

Ratio of alcohol to water in the second glass = 2:3

This can be written in a fraction as :-

$\color{olive} = \frac{2}{3}$

Ratio of water in the third glass , when all the alcohol and water in the first and second glass is poured into it :-

$= \frac{1}{4} + \frac{2}{3}$

$= \frac{(1 \times 3)}{12} + \frac{(2 \times 4)}{12}$

$= \frac{1}{12} + \frac{8}{12}$

$= \frac{9}{12}$

$= \frac{9 \div 3}{12 \div 3}$

$\color{hotpink} = \frac{3}{4}$

This fraction can be written in a ratio as :-

$\color{olive} = 3 : 4$

Therefore , the ratio of alcohol to water in the final mixture = 3:4 .