​The difference between two numbers is 18. If the difference between their squares is 360, find the larger number

Correct option is A

Given:

The difference between two numbers is 18.

The difference between their squares is 360.

Formula Used:

​$$a^2 - b^2 = (a - b)(a + b)$$​​

Solution:

Let the two numbers be a and b.

Given a - b = 18 and $$a^2 - b^2 = 360,$$​​

Substituting into the difference of squares identity:

360 = (a - b)(a + b)

360=18×(a+b)

a + b = $$\frac{360}{18}$$​ = 20

Now, we have two equations:

a – b = 18 and a + b = 20

From adding these equations;

we get a = 19 ,

By subtracting,

we get b = 1

Thus, the bigger number is 19