Question 896994
cost of the articles is x.


they sell for 72 and they sell for 84.


the gain on selling for 72 is 72 - x.
the gain on selling for 84 is 84 - x.


if the percent gain is double, then the gain is double.
conversely, if the gain is double, then the percent gain is double.


example:


cost is 100 and gain is 10.
percent gain is 10/100 * 100 = 10%.


cost is 100 and gain is 20.
percent gain is 20/100 * 100 = 20%.


double the gain gets double the percent gain.


back to your problem.


the gain on selling for 72 is 72 - x.
the gain on selling for 84 is 84 - x.


since the gain from selling at 84 is double the gain from selling at 72, you get the following formula:


(84 - x) = 2 * (72 - x)


you want to solve for x in this formula which will tell you what the cost of the articles was.


simplify to get 84 - x = 144 - 2x


add 2x to both sides of this equation and subtract 84 from both sides of this equation to get:


2x - x = 144 - 84


simplify to get:


x = 60


that's the cost of the articles.


when you sell at 84, your gain is 84 - 60 = 24 which is equal to 24/60 * 100 = 40% gain.


when you sell at 72, your gain is 72 - 60 = 12 which is equal to 12/60 * 100 = 20% gain.


the percent gain at 84 is double the percent gain at 72.