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

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Answer 1 · 2017-05-03T18:25:16

$53.76 %$ $53.76%$

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

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

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

So the new square is:

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

So then the net increase in the square is:

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

And the percentage increase is given by:

$\frac{336}{625} x^{2} \cdot \frac{1}{x^{2}} \cdot 100 = \frac{1344}{25} = 53.76 %$ $336/625 x^2 * 1/x^2 * 100 = 1344/25=53.76%$

If a number, xx is increased by 24% then what is the percentage increase in x2x^2?