The sum of two numbers is 75 and the difference of their squares is 300. Find the difference between the two numbers.

Correct option is A

Given:

The sum of two numbers is 75

The difference of their squares is 300.

Formula Used:

$$(x^2 -y^2)=(x+y)(x-y)$$​

Solution:

Let, the two numbers be $$x$$​ and $$y$$​​

Sum = $$x+y=75$$

Difference of their squares = $$x^2-y^2=300$$

Substitute the values in the formula,

​$$300=75(x-y)$$

$$\dfrac{300}{75}=(x-y)$$

​$$x-y=4$$​​

Therefore, the difference between two numbers is $$4$$.

Thus, the correct option is A.