Question

The sum of two numbers is $40$ and difference between them is $14$. Find the numbers.

Answer 1

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

Therefore,

$x+y=40.....\left(1\right)$

$x-y=14.....\left(2\right)$

Adding equation $\left(1\right)$ and $\left(2\right)$, we have

$(x+y)+(x-y)=40+14$

$2x=54$

$\Rightarrow x=\frac{54}{2}=27$

Substituting the value of $x$ in equation $\left(1\right)$, we have

$27+y=40$

$\Rightarrow y=40-27=13$

Hence the required numbers are $27$ and $13$.