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
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.
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.
Option B is the correct option.