The difference between two numbers is 9 and the difference between their squares is 207. The numbers are

Let the numbers be $$x$$ and $$y$$

Difference between two numbers = $$(x-y)=9$$ ----------(i)

Difference between their squares = $$x^2-y^2=207$$

=> $$(x-y)(x+y)=207$$

Substituting value from equation (i), we get :

=> $$9 \times (x+y)=207$$

=> $$(x+y)=\frac{207}{9}=23$$ ------------(ii)

Adding equations (i) and (ii),

=> $$2x=9+23=32$$

=> $$x=\frac{32}{2}=16$$

Substituting it in equation (ii), => $$y=23-16=7$$

$$\therefore$$ The two numbers are 16 and 7

=> Ans - (B)