If 80% of x = 40% of y, then x : y is equal to

When two percentage expressions of different quantities are set equal, p% of x = q% of y, the ratio x : y equals the inverse of the percentage figures, that is x : y = q : p. This follows directly from writing each percentage as a fraction of 100 and solving for x divided by y.

1. Write the given equation using the percentage-to-fraction conversion: 80% of x = 40% of y becomes (80/100)x = (40/100)y.

2. Simplify both fractions: 0.8x = 0.4y.

3. Isolate the ratio x/y by dividing both sides by y and then by 0.8: x/y = 0.4/0.8.

4. Reduce the fraction 0.4/0.8 to its lowest terms: x/y = 1/2, so x : y = 1 : 2.

Substitute x = 1 and y = 2 back into the original statement to confirm: 80% of 1 = 0.8, and 40% of 2 = 0.8 — the two sides match, verifying that x : y = 1 : 2 satisfies the given condition.