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Puzzled

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I have recently been given a job in Sales, and I really enjoy it. Math has never been a strong point and I struggle with percentages.

I had an embarrassing experience the other day, where my manager jokingly asked me in front of everyone ‘If our product cost $100 and we want to make 50% Gross profit margin, what the selling price?’ I said ‘$150’ but I am told the answer is $200.

I have found online that the calculation is:

$100 / 0.5 = $200

I seem to be using a mark-up calculation.

$100 x 1.5 = $150

Is there any easy way to calculate margin in your head?

Why there is a difference, and businesses don’t just use mark up?

Thanks everyone.