Question

The difference between two numbers is $5$ and difference in their squares is $65$. The larger number is

• A. $9$
• B. $10$
• C. $11$
• D. $12$

Answer 1

The correct option is A $9$

Difference between two numbers is 5.

Let larger number be $x$

$\therefore$ Other smaller number $=x-5$
Also given that the difference between there squares is 65
$\therefore (x{)}^2-(x-5{)}^2=65$

$\Rightarrow x^2[x^2+25-10x]=65$
$\Rightarrow x^2-x^2-25+10x=65$

$\Rightarrow 10x=90$
$\therefore x=9$

$\therefore$ Larger number $=x=9$