Question

The sum of two positive integers multiplied by the bigger number is $204$, and their difference multiplied by the smaller number is $35$. The numbers are :

• A. $12,5$
• B. $13,4$
• C. $14,3$
• D. $24,10$

Answer 1

Answer: (A)

$12,5$

$\Rightarrow$ Let the numbers be $x$ and $y$ such that $x>y.$

According to the question,

$\Rightarrow$ $x(x+y)=204$

$\Rightarrow$ $x^2+xy=204$ ------ ( 1 )

Again according to the question,

$\Rightarrow$ $y(x-y)=35$

$\Rightarrow$ $xy-y^2=35$ ------ ( 2 )

Subtracting ( 2 ) from ( 1 ), we get,

$\Rightarrow$ $x^2+y^2=169$

So here, $x^2=144$ and $y^2=25$

$\therefore$ $x=12$ and $y=5$

$\therefore$ The numbers are $12,5$