Final answer:
Assuming the third number as 100, the first number is 125 and the second number is 140. Their ratio simplifies to 25:28 after dividing both numbers by the greatest common divisor.
Step-by-step explanation:
Let's assume the third number (the base number we are comparing to) is 100. If the first number is 25% greater than this third number, it would be 125 (because 25% of 100 is 25, so we add this to 100). Similarly, if the second number is 40% greater than the third number, it would be 140.
To find the ratio of two numbers that are greater than a third number by certain percentages, we can use a proportion. Let's say the third number is x. The first number is x + 25% of x, which can also be written as x + 0.25x. Simplifying this expression gives us 1.25x. The second number is x + 40% of x, which is x + 0.40x. Simplifying this expression gives us 1.40x. So the ratio of the two numbers is 1.25x : 1.40x, or simplifying further, 5 : 7.
To find the ratio of the first number to the second number, we set up the ratio as 125:140. This ratio can be simplified by dividing both numbers by their greatest common divisor, which is 5. Thus, the ratio of the two numbers simplifies to 25:28.