Question

The sum obtained when two positive integers are multiplied by the bigger number is 204, and their difference when multiplied by the smaller number is 35. What are the two numbers?

• A. 12, 5
• B. 13, 4
• C. 14, 3
• D. 24,7
• E. Cannot be ascertained

Answer 1

The correct option is A

12, 5

Let the numbers be $x$ and $y$ such that $x>y$.
Then, $x\left(x+y\right)=204\Rightarrow x^2+xy=204....\left(i\right)y\left(x-y\right)=35\Rightarrow xy-y^2=35....\left(ii\right)$
Subtracting (ii) from (i), we get : $x^2+y^2=169.$
The only triplet satisfying this condition is (12, 5 ,13).
$\therefore x=12,y=5$.