The sum of the squares of two positive integers is 1025 and difference of their squares is 225 . The difference of the numbers is what percent of the product of these numbers ?

Correct option is C

Given:
Sum of squares = 1025
Difference of squares = 225
Formula Used:
​$$a^2 + b^2 = X$$​​
​$$a^2 - b^2 = Y$$​​
Percentage = $$\frac{Difference}{Product} × 100$$​​
Solution:
Let the two positive integers be a and b (where a > b).
​$$a^2 + b^2 = 1025$$​​
​$$a^2 - b^2 = 225$$​​
Add the two equations to solve for $$a^2:$$​​
​$$2a^2 = 1250$$​​
​$$a^2 = 625 \implies a = 25$$​​
Subtract the second equation from the first to solve for $$b^2:$$​​
​$$2b^2 = 800$$​​
​$$b^2 = 400 \implies b = 20$$​​
Calculate the difference and the product of the numbers.
Difference = a - b = 25 - 20 = 5
Product = a × b = 25 × 20 = 500
Calculate the percentage.
Percentage = $$\frac{5}{500} × 100 = 1\%$$​​
Final Answer
So the correct answer is (c)