The flask contains a salt solution with a concentration of p%. 1/3 of the solution is poured from the flask

The flask contains a salt solution with a concentration of p%. 1/3 of the solution is poured from the flask into a test tube, and the rest is evaporated until the percentage of salt doubles. When the separated part of the solution was again poured into the flask, it turned out that the salt content in the resulting solution had become (p + 15)%. Determine the concentration of the original solution.

The solution of the problem.

This problem will be solved using an equation with an unknown variable p.

1. Let us denote by m the initial mass of the solution.

2. Find the mass of the solution poured into the test tube.

1/3 m.

3. Find the mass of the solution remaining in the flask

m – 1/3 m = 2/3 m.

4. Find the mass of the solution remaining in the flask after evaporation.

2/3 m: 2 = 1/3 m.

5. Find the mass of the solution after refilling from the test tube.

1/3 m + 1/3 m = 2/3 m.

6. The mass of salt after adding the solution from the test tube will be equal to the initial one – the salt has not gone anywhere.

7. Find the concentration of the new solution.

p * m: 2/3 m = 1.5r.

8. Let’s compose and solve the equation.

1.5p = p + 15;

0.5p = 15;

p = 30.

Answer. The concentration of the initial solution is 30%.