How to prepare 1 percent solution of potassium permanganate from 500 g of 5% solution?

Given:
ω1 (KMnO4) = 5%
m1 solution (KMnO4) = 500 g
ω2 (KMnO4) = 1%

To find:
m (H2O) -?

Decision:
1) To prepare a 1% solution of KMnO4 from 5%, a certain amount of water must be added. Find the ratio of the masses of the KMnO4 solution and water (use the cross rule):

2) Find the mass of H2O (make up the proportion):
If for the preparation of a 1% solution of KMnO4 it is necessary to take 1 g of a 5% solution and 4 g of H2O, then (x) g of H2O must be added to 500 g of 5%:
14
500 – x
x = 500 * 4/1 = 2000;

m (H2O) = x = 2000 g = 2 kg.

Answer: The required mass of H2O is 2 kg.