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

Analyze the question: Two numbers are 35% and 80% more than a third number. We need the ratio of the first two numbers.

Concept: "x% more than a number N" means N + x% of N = N(1 + x/100).

Solution:

Let the third number be N.

• First number = N + 35% of N = 1.35N
• Second number = N + 80% of N = 1.80N

Ratio of first to second = 1.35N : 1.80N = 1.35 : 1.80

Multiply by 100: 135 : 180

Divide both by 45: 135 ÷ 45 = 3 and 180 ÷ 45 = 4

So the ratio = 3 : 4

Checking against the options: This matches option B.

Notice that the options 7 : 16 and 16 : 7 come from mistakes such as using 35 : 80 directly (which simplifies to 7 : 16). That ignores the "more than" part, which means you must add the percentage to 100%.

Tip: For "x% more than", use (100 + x)%. So 35% more becomes 135%, and 80% more becomes 180%. Then simplify the ratio 135 : 180. Also, read the order carefully: the question asks for the first number to the second, which gives 3 : 4, not 4 : 3.