Calculating two numbers based on percentage of a given number

Question

So I have two numbers one is the main number, lets say 53. I want to find two corresponding numbers automatically given that the two numbers should equal to 53 and have a gap of 10.4%. So let me do one example.

Original Number = 53.37 (Known) Gap = 10.4 (Known)

First number = 28.15 Second number = 25.22 Gap between the two = (28.15-25.22)/ 28.15 (first number) = 10.4% 28.15 (First number) + second number (25.22) = 53.37 (original number)

I did this example by hand. Now I have a lot of other equations to solve like this. I want to do them automatically. E.g. Original Number =264 Gap = 11.5

Original Number = 800 Gap = 12.5

Is there any way to do this automatically in excel? Any help would be appreciated

Answer 1

This is not a statistics question, but if the sum is $S$ and the gap is $g\%$ of the larger value then

• the larger value is $\dfrac{1}{2-\frac{g}{100}}S$
• the smaller value is $\dfrac{1-\frac{g}{100}}{2-\frac{g}{100}}S$

so in your example $\dfrac{1}{2-\frac{10.4}{100}}\times 53.37 \approx 28.15$ and $\dfrac{1-\frac{10.4}{100}}{2-\frac{10.4}{100}}\times 53.37 \approx 25.22$