The question is as follows:
Question is that how many % profit in euros decreases.
Selling price of 70€ includes 40% profit. Price was decreased by 10%. How many % does the profit decrease?
My math is
x*1.4=70
x=50
70*.9=63
63-50=13
13/20=.65 therefore profit is only 65% of the original profit,
meaning the profit has decreased 35%, this answer was assessed as incorrect.
What did I calculate incorrectly, and what is the correct way to solve this problem?
On
As you calculated:
Old selling price included $40$% profit is $70$ euros,
Old selling price not included profit is $50$ euros, at this point it is correct.
An extra thing you will need is the original profit is worth $20$ euros, but after the discount, the price is now only $63$ euros (which you also did correctly), so:
New selling price not including profit: $63 \div 1.4 =45$ euros
Profit of the new selling price: $63-45=18$ euros
The old selling price profit is $20$ euros, but the new selling price profit is $18$ euros, so the profit is decreased by $10$%.
I think it is unclear what "includes $40\%$ profit" means:
One interpretation: "$40\%$ of the $70$ is profit"
Assuming that, let $C$ be your cost for the object. We can compute $C$...we are given that $.4\times 70=28$ represented profit so $$C=70-28=42$$
If we reduce the selling price by $10\%$ we get a new selling price of $63$. That would give us a profit of $$P_2=63-42=21$$
Thus the profit decreases from $28$ to $21$ which represents a drop of $7$ which is $25\%$ of the original profit.
Another interpretation "selling at $70$ would give a $40\%$ profit over your cost"
This is more akin to what was done in the original post.
Assuming that then we get, as in the post, that the original cost was $50$ and the profit $20$. If we reduce the selling price to $63$ then the new profit is $13$ which represents a $26\%$ profit over cost (which of course is still $50$). Thus we have a $14\%$ drop in profit in this scenario.