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.
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