averages topic

Question

a chemist has two solutions , one of which is 40% acid and the other is 20% acid . how many liters of solution with 20% acid should the chemist mix to get 10 liters of solution that is 25%

(a)8.5 liters 

(b)5.5 liters 

(c)6.5 liters 

(d)7.5 liters 

Answer 1

The amount of acid in x liters of 40% acid solution is 0.4x.

 

If x liters of 40% acid are used, 10 - x liters of 20% acid will be used to get a total of 10 liters. The amount of acid in 10 - x liters of 20% acid solution is 0.2(10 - x).

 

The amount of acid in 10 liters of 25% acid solution is 0.25(10) = 2.5 liters.

 

 

 

We know that the amount of acid in the two solutions we're mixing (40% and 20%) needs to equal the amount of acid in the final solution (25%). So:

 

0.4x + 0.2(10 - x) = 2.5

0.4x + 2 - 0.2x = 2.5

0.2x + 2 = 2.5

0.2x = 0.5

x = 2.5

 

So, you need x = 2.5 liters of 40% solution and 10 - x = 10 - 2.5 = 7.5 liters of 20% solution.