Question 1089236
the regular price is x and the regular weight is y.


the regular price per pound is therefore x/y.


the new price is .9 * x and the new weight is .8 * y.


the new price per pound is therefore .9 * x / (.8 * y) = .9/.8 * x/y which is equal to 1.125 * x/y


the customer is paying 12.5% more on a price per pound basis.


put this into numbers and you should be able to see what i mean.


you sell a chocolate bar for 10 dollar and it contains 1 pound of chocolate.


you reduce the price to 9 dollars but the chocolate bar now only contains .8 pounds of chocolate.


the customer is paying less money for the chocolate bar but he's getting even less chocolate.


the cost per pound of chocolate in the original bar was 10/1 = 10 dollars per pound.


the cost per pound of chocolate in the new bar is 9/.8 = 11.25 dollars per pound.


that's an increase in price per pound of chocolate of 1.25 over 10 dollars which is equal to .125 which is equal to 12.5%.


the shopkeeper makes 12.5% profit over the regular price per pound of chocolate.


example:


he wants to sell 100 pounds of chocolate.


when each bar of chocolate is 1 pound, and he's charging 10 dollars for each bar, then he can sell 100 bars at 10 dollars apiece to make 1000 dollars.


when each bar of chocolate is .8 pounds, and he's charging 9 dollars for each bar, then he can sell 125 bars of chocolate at 9 dollars apiece for a total of 1125 dollars.


his profit is 125 dollars over what he would have made with the original price and weight.


this is equal to 125/1000 * 100 = 12.5%.


note that 10% loss on the cost price is equal to (1 - .10) * cost price which is equal to .9 * original cost price.


note also that 20% loss on weight is equal to (1 - .2) * weight which is equal to .8 * original weight.