Question

The difference of two numbers is $3$ and the difference of their square is $69$. Find the numbers.

• A. $3$ and $9$
• B. $13$ and $10$
• C. $11$ and $18$
• D. $5$ and $2$

Answer 1

Answer: (B)

$13$ and $10$

Let the two numbers be $x$ and $y$.
Then, $x-y=3...\left(i\right)$
and $x^2-y^2=69$
$\Rightarrow (x-y)(x+y)=69$
$\Rightarrow 3(x+y)=69$ $($from $\left(i\right))$
$\Rightarrow x+y=23...\left(ii\right)$
Adding $\left(i\right)$ and $\left(ii\right)$, we get
$2x=26\Rightarrow x=13$
On putting $x=13$ in $\left(ii\right)$, we get
$13+y=23\Rightarrow y=10$
Hence, the given numbers are $13,10$