Question : The difference between two numbers is 9 and the difference between their squares is 207. The numbers are:
Option 1: 17 and 8
Option 2: 16 and 7
Option 3: 15 and 6
Option 4: 15 and 7
Correct Answer: 16 and 7
Solution :
Given: The difference between the two numbers is 9.
The difference between their squares is 207.
Let the numbers be $x$ and $y$.
Difference between the numbers $(x-y)=9$ ----------------------(1)
Difference between their squares $(x^{2}-y^{2})=207$
$⇒(x-y)(x+y)=207$ ---------------------------(2)
Substituting the value of $(x-y)$ in equation (2)
$⇒9×(x+y)=207$
$⇒(x+y)=23$ -------------------------(3)
Adding equations (1) and (3), we get,
$⇒2x=32$
$\therefore x=16$
So, $y=(23-16)=7$
Hence, the correct answer is 16 and 7.
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