Question

A man mixes 10 liter of alcohol with 40 liters of water. After selling one-fourth of this mixture, he adds alcohol to replenish the quantity that he has sold. What is the current proportion of alcohol to water

Answer 1

Answer:

The ratio of alcohol to water is 1 : 3

Explanation:

Ratio of alcohol and water in initial mixture

                                   10 : 40

                         or        1 : 4

after selling one forth

Water left = 40 × $\frac{3}{4}$ = 30 liters

Alcohol left = 10 × $\frac{3}{4}$ = 7.5 liters

Man replenishes alcohol to 10 liters.

Now new ratio is

                  Alcohol : Water

                     10 : 30

   or                1 : 3               Answer

Answer 2

Answer: The current proportion of alcohol to water is 2 : 3

Solution:

Step 1.

Initially alcohol = 10 litres

and water = 40 litres

Total mixture = (10 + 40) litres = 50 litres.

In this mixture,

fraction of alcohol = 10/50 = 1/5

& fraction of water = 40/50 = 4/5

Step 2.

1/4 of the mixture, i.e., 50/4 litres = 12.5 litres of mixture has been sold.

Remaining mixture

= (50 - 12.5 litres = 37.5 litres

In this mixture,

alcohol = 37.5 * 1/5

= 7.5 litres

& water = 37.5 * 4/5

= 30 litres

Step 3.

After selling 12.5 litres of the mixture, 12.5 litre of alcohol has been added.

Now alcohol = (7.5 + 12.5) litres

= 20 litres

and water = 30 litres

Therefore, the current proportion of alcohol to water is

= 20 : 30 = 2 : 3