Question

The sum of two numbers is $1400$. The number obtained by decreasing the bigger number by $20\%$ is equal to the number obtained by increasing the smaller number by $20\%$. Find the numbers.

Answer 1

Let the numbers be $x$ and $y$ with $x>y$.

Then according to the problem,

$x+y=1400$ ......(1).

Also given,

$\frac{80x}{100}=\frac{120y}{100}$

or, $2x=3y$

or, $x=\frac{3y}{2}$.

Using this values in (1) we get,

$\frac{5y}{2}=1400$

or, $y=5600$.

Then $x=8400$.

So the numbers are $8400$ and $5600$.