3 kg of a solution contains 40% of alcohol by weight. How much alcohol should be added to obtain a solution containing 50% of alcohol by weight?

A. 0.3 kg

B. 0.6 kg

C. 0.75 kg

D. 1.5 kg

E. 3.75 kg

### 3 Answers | Add Yours

Let us say we need to add xkg of alcohol to make it 50% by weight.

Amount of alcohol in 40% solution `= 40/100xx3 = 1.2kg`

In the new mixture the weight percentage of alcohol is 50%.

In this solution we have (1.2+x) of alcohol and the total weight of the solution would be 3+x.

`(1.2+x)/(3+x)xx100 = 50`

`2(1.2+x) = 3+x`

`x = 0.6`

*So we need to add another 0.6kg of alcohol. Correct answer is at option B.*

Option B is the correct option.

3 kg of a solution contains 40% of alcohol by weight. Let the weight of alcohol to be added to create a solution with 50% alcohol be x kg. When x kg of alcohol is added to 3 kg of a solution with 40% alcohol by weight, the total weight of the solution is 3 + x and the weight of alcohol is 0.4*3 + x = 1.2 + x

As the new mixture has 50% alcohol by weight, (1.2 + x)/(3 + x) = 0.5

1.2 + x = 1.5 + 0.5*x

0.5*x = .3

x = 0.6

0.6 kg of alcohol should be added to obtain the required solution of alcohol.

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes