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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?

BaronTruth
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  • Based on a quick read your reasoning looks OK if the $40%$ profit is based on the selling price. If it's based on the cost then a deleted answer is right. I think the question is ambiguous. Can you edit the question to tell us what the correct answer is? – Ethan Bolker Mar 14 '18 at 14:04
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    I think it is not clear what "includes $40%$ profit" means. I initially read that as saying that $40%$ of the sale price was profit but your interpretation is sensible as well. – lulu Mar 14 '18 at 14:06
  • @lulu I was about to add my comment to your deleted answer. Please undelete, and perhaps include both calculations. – Ethan Bolker Mar 14 '18 at 14:08
  • 40 - 26 = 14 ?, i think the question is a bit unclear. – kayush Mar 14 '18 at 14:09
  • @EthanBolker I have undeleted and provided two calculations though I think others are possible. – lulu Mar 14 '18 at 14:25

2 Answers2

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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.

lulu
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  • Almost. In the second scenario the drop in profit is $35%$ as the OP said. Your answer restates that as a $14$ percentage point drop in profits, from $40%$ to $26%$. – Ethan Bolker Mar 14 '18 at 14:30
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    @EthanBolker Again, I think the phrasing is unclear. I read "How many % does the profit decrease?" the way I computed it. I don't think there is a mathematical disagreement here...just one of language. – lulu Mar 14 '18 at 14:34
  • I agree. And I think the OP knows just what he's doing, better than the questioner. I particularly like his $1.4x=70$ for finding the cost. – Ethan Bolker Mar 14 '18 at 14:36
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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 $10$%.

user061703
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