Question

20 l of mixture contains alcohol and soda in the ratio 6 : 2. If 4l of this mixture be replaced by 4 l of alcohol the ratio of alcohol to soda in the new mixture?

Answer 1

The ratio of alcohol to soda in the new mixture = 4 : 1

Given :

• 20 l of mixture contains alcohol and soda in the ratio 6 : 2.

• 4 l of this mixture be replaced by 4 l of alcohol

To find :

The ratio of alcohol to soda in the new mixture

Solution :

Step 1 of 3 :

Calculate the amount of alcohol and soda in 20 l mixture

The ratio of alcohol to soda in the mixture

= 6 : 2

= 3 : 1

In 20 l mixture -

$\displaystyle \sf{ Amount \: of \: alcohol = 20 \times \frac{3}{3 + 1} = 20 \times \frac{3}{4} = 15 \: l }$

$\displaystyle \sf{ Amount \: of \: soda = 20 \times \frac{1}{3 + 1} = 20 \times \frac{1}{4} = 5 \: l }$

Step 2 of 3 :

Calculate the amount of alcohol and soda in 4 l mixture

The ratio of alcohol to soda in the mixture

= 6 : 2

= 3 : 1

In 4 l mixture -

$\displaystyle \sf{ Amount \: of \: alcohol = 4 \times \frac{3}{3 + 1} = 4\times \frac{3}{4} = 3 \: l }$

$\displaystyle \sf{ Amount \: of \: soda = 4 \times \frac{1}{3 + 1} = 4 \times \frac{1}{4} = 2 \: l }$

Step 3 of 3 :

Calculate ratio of alcohol to soda in the new mixture

It is given that 4 l of this mixture be replaced by 4 l of alcohol

In the new mixture -

Amount of alcohol = (15 - 3 + 4) l = 16 l

Amount of soda = (5 - 1) l = 4 l

Hence the ratio of alcohol to soda in the new mixture

= 16 : 4

= 4 : 1

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