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mathreverse-engineeringpercentage

Maths Two Percentage Increases - Any Takers

Maths Puzzle

A = 10 (COST)
B = 20 (Sell Price)
C = 15% (Fee) 
D = Tax at 20% or 1/6th if you are taking it away
E = Margin


B x C = 3.60
B / 6 in Reverse = 3.33
E = B - A - (B x C) - (B  / 6) = 3.07

Ok The above works correct when i i provide B Sell Price

I want a formula that will Give me E, If i say E = 3.07 It says B = 20

How would i do that, the math

Any boffins can help

Thanks

Solution

  • First:

    • You did not use D: I suppose instead of B / 6, it should read B x D, where D can be either 20% or 16,666...%

    • There is a mistake: B x C is not 3.60 for the given values (B=20, C=15%), it is 3.

    This is a matter of mathematical deduction:

    Given the equation:

    E = B - A - (B x C) - (B x D)

    Add A to both sides:

    E + A = B - (B x C) - (B x D)

    Isolate B:

    E + A = B x (1 - C - D)

    Divide both sides by (1 - C - D). Condition: C + D cannot equal 100%

    (E + A) / (1 - C - D) = B

    So there is your formula for calculating B. Take note of the condition: this only holds true when C + D is not equal to 100%.