# If a number, x is increased by 24% then what is the percentage increase in x^2?

May 3, 2017

53.76%

#### Explanation:

We have the original number $x$, and its square ${x}^{2}$

If this number is increased by 24% then the new value is:

$x + \frac{24}{100} x = \frac{124}{100} x = \frac{31}{25} x$

So the new square is:

${\left(\frac{31}{25} x\right)}^{2} = \frac{961}{625} {x}^{2}$

So then the net increase in the square is:

$\frac{961}{625} {x}^{2} - {x}^{2} = \frac{336}{625} {x}^{2}$

And the percentage increase is given by:

 336/625 x^2 * 1/x^2 * 100 = 1344/25=53.76%