Question

The sum of two numbers is $25.$ One of the numbers exceeds the other by $5.$ Find the numbers.

• A. $16$ and $9$
• B. $10$ and $15$
• C. $12$ and $17$
• D. $20$ and $5$

Answer 1

The correct option is B $10$ and $15$

Let the two numbers be $x$ and $y,$
Given, sum of them is $25$
$\therefore x+y=25\dots \left(i\right)$
and $y$ exceeds the $x$ by $5$
$\therefore y=x+5\dots \left(ii\right)$

Step 1: Find the value of x.
Substituting $y=x+5$ in $\left(i\right),$ we get
Equation $\left(i\right)$ $\to$ $x+y=25$
$x+x+5=25$
$\Rightarrow 2x=25-5=20\Rightarrow x=\frac{20}{2}\Rightarrow x=10$

Step 2: Now, Find the value of y
Substitute $x=10$ in equation $\left(ii\right)$
Equation $\left(i\right)$ $\to$ $y=5+x$
$y=5+10$
$\Rightarrow y=15$
$\therefore x=10,y=15$

Therefore, the two numbers are $10$ and $15.$