Question

In a lab a 30% acid solution is being mixed with a 5% acid solution to create a 10% acid solution. What is the ratio of the amount of the 30% solution to the amount of 5% solution used to create the 10% solution

Answer 1

1 : 4

Explanation:

For a problem of this nature, a simple diagram makes the solution trivially easy. In the attached, the constituent concentrations are listed on the left, the solution concentration is in the middle, and the numbers on the right are the differences along the diagonals. These are the ratios of the respective solutions on the left.

That is, the ratio of 30% solution to 5% solution is 5 : 20 or 1 : 4.

Answer 2

1:4

Explanation:

Let it be:

• 30% solution = x
• 5% solution = y

then

• 10% solution = x + y

----------

Amount of acid:

• 0.3x + 0.05y = 0.1(x+y)
• 0.3x + 0.05y = 0.1x + 0.1y
• 0.2x = 0.05y
• 20x = 5y
• 4x = y
• x/y = 1/4

So the ratio of 30% solution to the 5% solution is 1:4