Question

The difference between two integers is 5.Their product is 500. Find the numbers.

• A. $15,20$
• B. $20,25$
• C. $30,25$
• D. $21,26$

Answer 1

Answer: (B)

$20,25$

Let two numbers be $x$ and $y$.

Since,

$x-y=5$ $........\left(1\right)$

$xy=500$ $........\left(2\right)$

We know that

$(x+y{)}^2=(x-y{)}^2+4xy$

$(x+y{)}^2=5^2+4\times 500$

$(x+y{)}^2=25+2000$

$(x+y{)}^2=2025$

$(x+y)=45$ $.........\left(3\right)$

On solving equation $\left(1\right)$ and $\left(2\right)$, we get

$x=25,y=20$

Hence, this is the answer.