calculate the margin in percent

Question

My brain is fried and don't know where else to get the answer, so please be nice :-)

I can calculate the margin in percent when I got the original number 12.27 and the new number 27.968. I can do this to get the margin in percent:

27.968 - 12.27 = 15.698
15.698 / 27.968 = 0.561284325
0.561284325 * 100 = 56.1284325

But I need to find out what the new number should be without knowing it beforehand. Also I know the percent should be 56%.

I can do this, but that is clearly wrong (the result should be 27.968):

12.27 * 1.56 = 19,1412

Answer 1

If I understood correctly, you want something which gives you back the value you're looking for, based on some given information.

Considering that:

• $n$ represents your New number
• $o$ represents your Original number
• $v$ represents your Known percentage

And knowing that $\frac{100(n - o)}{n} = v$, we can solve for $n$, step by step, as follows:

$\frac{100(n - o)}{n} = v$

$100(n - o) = nv$

$100n - 100o = nv$

$-100o = -100n + nv$

$-100o = n(-100 + v)$

$\frac{-100o}{-100 + v} = n$

$-\frac{100o}{v - 100} = n$

Substituting with the actual values, we obtain:

$n = -\frac{100(12.27)}{56.12843249427917 - 100}$

$n = 27.968$