Sarika Z.
asked • 08/26/16Profit and loss
can anybody tell me why my answer is not matching in this way.
Q. For an item the profit is 40% when the discount is 30%. What is the profit when the discount is 40%.
my method:
100 be the base price. 30% discount means new price is 70. Let x be the cost price.
X(140/100)=70
x=50
so with 40% discount price is 60. So
(10/50)*100=20%
but the answer is 30%
can anybody tell me what I did wrong.
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2 Answers By Expert Tutors
Kendra F. answered • 08/26/16
Tutor
4.7
(23)
Patient & Knowledgeable Math & Science Tutor
I believe you have the correct answer.
30% off selling price = 40% profit
0.7S = 1.4C
if the selling price, S is 100$ the customer get's it for 70$ and the store bought the item for 50$ = C and made a profit of 20$ on the item.
20$/50$ = 0.4
40% profit
If the selling price and cost remains the same but the discount is increased to 40% off.
0.6(100) = 50x
60 = 50x
60/50 = x
1.2 = x
profit is 20%
David W.
tutor
Kendra, as mentioned, the percentage is of the discounted price and not the cost.
I have a $100 item on sale for $70. That's a 30% discount. If my profit is 40%, that's of the $70, not the cost. The cost is 60% of the $70, or $42.
(70-42)/70 = 28/70 = 4/10 = 40% profit.
Now, I am selling it for $60. That's a 40% discount. (60 - 42)/60 = 18/60 = 3/10 = 30%.
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08/26/16
Kendra F.
If this is the solution, then I'd say this is a very poorly worded question..
Percent profit is 100 x profit/cost. Gross margin is 100 x profit/selling price.
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08/26/16
It took me a minute to figure it out!
The profit is a percentage of the sale price, not a percentage of the cost.
The cost is then 60% of the $70. (60/100)70 = $42.
Nooooow, your price with 40% off is still $60. 60 - 42 = 18. (18/60)100 = 30%.
Boom.
Sarika Z.
But shouldn't it be the same thing? Like isn't 140% of the cost supposed to give me the selling price? That's what we do in most of the sums. And is the profit always on the selling price and not on the cost price?
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08/26/16
David W.
tutor
Sarika, look at your own work. Taking 40% off $100 gives us $60, but 140% of $60 is $84.
Yes, the profit is a percentage of the selling price, not of the cost. Selling something that costs $60 to make for $100 gives us a profit of (40/100)100 = 40% and not (40/60)100 = 67%.
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08/26/16
David W.
tutor
Yes, the profit is a percent of the selling price and not the cost. If we sell something for $100 that costs $60, our profit is (40/100)100 = 40%, not (40/60)100 = 67%.
Also, remember that taking 40% off doesn't mean that our regular price is 140% of the sale price. Let's look again at our $60 item selling for $100. We saw that taking 40% off $100, but 140% of $60 is $84, because 40% of 60 is smaller than 40% of 100.
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08/26/16
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Kendra F.
08/26/16