Profit, Loss Dishonest seller

algebra-precalculus

You have shown what would happen if the seller diluted his sugar with 25% impurities (hence the larger profit margin).

We dilute the sugar 20%. 1000 g of pure sugar becomes 1200 g of debased sugar.

Or 1000g of debased sugar has $\frac {1000}{1.2} = 833.3 $g of pure sugar and $166.3$ g of additives.

We can check $\frac {166.6}{833.3} = 0.2$

We then sell 800 grams of the stuff. $\frac {800}{1.2} = 666.6g = \frac {2}{3} kg$ pure sugar.

The profit is $\frac {1}{3}$ £ the cost is $\frac 23$ £, the ratio $50\%$ margin.

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