Question

If the difference of two numbers is 3 and the difference of their squares is 39 then the larger number is :

• A. 8
• B. 9
• C. 12
• D. 13

Answer 1

The correct option is A 8

The two numbers be $a,b$ respectively.

According to equation,

$\therefore a-b=3⟶\left(1\right)$

$a^2-b^2=39$

$(a+b)(a-b)=39$

$(a+b)\times 3=39$

$(a+b)=13⟶\left(2\right)$

$a-b=3a+b=13$

On adding: $2a=16a=8$

putting $a$ in equation $\left(1\right)$

$a-b=38-b=3b=5$

$\therefore$ Large number is $8.$