Question

The sum of two number is $40$. If the smaller number is doubled, it becomes $14$ more than the larger number. Find the numbers

Answer 1

Let the larger number be $x$

and smaller number be $y$

As per the question, we have

$x+y=40$ ....(1)

and $2y=14+x$ ....(2)

Therefore, $y=\frac{14+x}{2}$ ....(3)

Substitute this value of $y$ in equation (1), we get

$x+\frac{14+x}{2}=40$

$\Rightarrow 2x+14+x=80$

$\Rightarrow 3x=80-14$

$\Rightarrow 3x=66$

$\Rightarrow x=22$

Put this value of $x$ in equation (3),

$y=\frac{14+22}{2}$

$\Rightarrow y=18$

therefore, the two numbers are $22$ and $18$.