100 g of water was added to a solution containing 40 g of salt, as a result of which the concentration

100 g of water was added to a solution containing 40 g of salt, as a result of which the concentration decreased by 2%, find the initial mass of the solution.

1. Let’s denote the initial mass of the solution by X.

2. Then the initial concentration of the solution in percent S1 = 40 / X * 100%.

3. The concentration of the solution after adding water S2 = 40 / (X + 100) * 100%.

4. The difference in concentration according to the condition of the problem S1 – S2 = 2%.

5. From this condition we obtain the equation of the problem: 40 / X * 100% – 40 / (X + 100) * 100% = 2%.

6. Let’s simplify this expression. We get a quadratic equation:
X ^ 2 + 100 * X – 20 * 100 * 100 = 0.

7. The discriminant equation D ^ 2 = 100 * 100 + 80 * 100 * 100 = 81 * 100 * 100.
Or, taking the square root, D = 9 * 100.

8. The roots of the equation are X = 400 and X = – 500. The negative root does not correspond to the condition of the problem. Therefore X = 400 g.

Answer: the initial mass of the solution is 400 g.