Two numbers are respectively 35% and 80% more than a third number. The ratio of the two numbers is

Let the third number be x. “35% more than x” means x plus 35% of x, which is 1.35x. “80% more than x” means x plus 80% of x, which is 1.80x.

So the ratio of the two numbers is 1.35x : 1.80x. The x cancels out, leaving 1.35 : 1.80. Multiply both sides by 100 to clear the decimals: 135 : 180.

Now divide both by their highest common factor, 45: 135 ÷ 45 = 3 and 180 ÷ 45 = 4. The ratio is 3 : 4. A quick test with x = 100 gives 135 and 180, and 135/180 = 3/4 ✓.