SOLUTION: A buys an article and sells it to B at the profit of 12%.B sells it back to A at price which A previously paid for it.What is B's percentage loss ?

Question 1097506: A buys an article and sells it to B at the profit of 12%.B sells it back to A at price which A previously paid for it.What is B's percentage loss ?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if the selling price is greater than the cost, then subtract the cost from the selling price and that's your profit.

if the selling price is less than the cost, then subtract the selling price from the cost and that's your loss.

your percent profit is equal to 100 times your profit divided by your cost.

your percent loss is equal to 100 times your loss divided by your cost.

in your problem:

let the cost to A be equal to x.

A sells it to B at a 12% profit.

the profit to A therefore has to be .12 * x and the selling price to B has to be equal to 1.12 * x.

the cost to B is therefore 1.12 * x.

B sells it back to A at a selling price of x, which is the original cost to A.

the loss to B is therefore .12 * x.

the loss to B is the same as the profit to A.

however, ........

the percent profit to A is profit / cost = .12 * x / x = .12 = 12%.

the percent loss to B is loss / cost = .12 * x / (1.12 * x) = .12 / 1.12 = 10.71%.

the loss to B is the same as the profit to A, but the percent loss to B is different from the percent profit to A because the denominator in the equation is different.

that's because the cost to A was x while the cost to B was 1.12 * x.

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