Question

Amy is two years older than Bill. The square of Amys age in years is $36$ greater than the square of Bills age in years. What is the sum of Amys age and Bills age in years?

• A. $17$
• B. $18$
• C. $19$
• D. $20$

Answer 1

The correct option is B $18$

As Amy(A) is two years older than Bill(B).i.e: $A=B+2$ ; $B=A-2$ and the square of Amys age in years is $36$ greater than the square of bills age.i.e: $A^2=B^2+36$
substituting $B=A-2$
Then, $A^2=(A-2{)}^2+36$$\Rightarrow A^2=A^2-4A+4+36$
$\Rightarrow A=10$
As, $B=A-2=10-2=8$
Therefore, the sum of Amys age and Bills age in years $=10+8=18$