How to solve a percentage word problem for profit?

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To solve the percentage word problem, the original selling price of goods was incorrectly calculated based on the wrong approach. The correct method involves letting X represent the original price, where selling at a loss of 10% results in a sale price of Rs 153. The equations 0.90X = 153 and Z = X + 0.20X were established, leading to the correct original price of Rs 170. From there, a 20% gain calculation gives a selling price of Rs 204. Understanding the correct application of percentage calculations is crucial for solving such problems accurately.
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Homework Statement


A person lost 10% when he sold goods at Rs 153 for how much should he sell them to gain 20% .

Homework Equations

The Attempt at a Solution


0.10(153)= 15.3

153+15.3= 168.3 ( the price of product for no profit)

0.2(168.3)=33.6
(168.3+33.6)= 201.9 rupees is the 20% gain ?

have i done the problem correctly , or is their a more general way to do this.
 
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In your first step, you have taken 10% of the sale amount. Is that really what you want to be doing? Think about it.
 
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phinds said:
In your first step, you have taken 10% of the sale amount. Is that really what you want to be doing? Think about it.
negative 10 percent ?
 
Last edited:
alijan kk said:
negative 10 percent ?
IS MY ANS CORRECT?
No. You are taking 10% of the wrong thing. @phinds hint is a good one.
EDIT: I would have been more clear if I said that you are using 10% the wrong way.
 
alijan kk said:
negative 10 percent ?
IS MY ANS CORRECT?
No, it is not correct (and no need to be yelling with all capital letters...).

As @phinds was hinting, your original method to calculate the starting amount is not correct (you have made a very common error for students learning to work this type of problem.

If I have 100 of something, what is 10% less than that? Can you apply that same logic to this problem? Let X be the starting amount in this problem, and try again to do the calculation, using the hint I have provided. :smile:

Dang it, beaten out y @FactChecker yet again... :smile:
 
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berkeman said:
No, it is not correct (and no need to be yelling with all capital letters...).

As @phinds was hinting, your original method to calculate the starting amount is not correct (you have made a very common error for students learning to work this type of problem.

If I have 100 of something, what is 10% less than that? Can you apply that same logic to this problem? Let X be the starting amount in this problem, and try again to do the calculation, using the hint I have provided. :smile:

Dang it, beaten out y @FactChecker yet again... :smile:
i am sorry i still don't get it :(
 
berkeman said:
If I have 100 of something, what is 10% less than that? Can you apply that same logic to this problem? Let X be the starting amount in this problem
Use my hint. Let X be the starting amount, and Y is the amount that is discounted by 10%. Show that equation please. Then let Z be the amount that is 20% more than the starting amount. Can you show that equation please?

Then using those two equations that you have written out, you should be able to solve the problem with a little algebraic manipulation... :smile:

Please show all of your work so we can check it. Thank you.
 
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berkeman said:
Use my hint. Let X be the starting amount, and Y is the amount that is discounted by 10%. Show that equation please. Then let Z be the amount that is 20% more than the starting amount. Can you show that equation please?

Then using those two equations that you have written out, you should be able to solve the problem with a little algebraic manipulation... :smile:

Please show all of your work so we can check it. Thank you.
0.90X=Y

is this a correct equation
 
alijan kk said:
0.90X=Y

is this a correct equation
Yes, good so far! Keep on going...
 
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  • #10
berkeman said:
Yes, good so far! Keep on going...
original price is 170 !
yes thankyou . i am going.. not very well but ok
 
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  • #11
berkeman said:
Use my hint. Let X be the starting amount, and Y is the amount that is discounted by 10%. Show that equation please. Then let Z be the amount that is 20% more than the starting amount. Can you show that equation please?

Then using those two equations that you have written out, you should be able to solve the problem with a little algebraic manipulation... :smile:

Please show all of your work so we can check it. Thank you.
Z= 170+0.20(170)= 204 yes this is the answer thankyou!
 
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  • #12
alijan kk said:
Z= 170+0.20(170)= 204 yes this is the answer thankyou!
Good work. :smile:

So do you see the issue now with your original approach? You need to find the original value before trying to add to it. Like I said, it is a common error as you start to learn this type of problem. But now you know what to look out for! :smile:
 
  • #13
alijan kk said:
Z= 170+0.20(170)= 204 yes this is the answer thankyou!
BTW, another way to write that is 1.2 * 170 = 204.
 
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  • #14
berkeman said:
BTW, another way to write that is 1.2 * 170 = 204.
hmm yes direct answer
 
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  • #15
alijan kk said:
hmm yes direct answer
i am sorry to post here , but i how can i use all maths symbol ? (to post calculus problems)
 
  • #16
alijan kk said:
i am sorry to post here , but i how can i use all maths symbol ? (to post calculus problems)
No worries, and good for you to want to start posting using math symbols. You can click on the sigma ∑ symbol in the toolbar at the top of the Edit window to get simple symbols for in-line text, and you can learn more about posting in LaTeX in the tutorial under INFO/Help-How To at the top of the page. :smile:
 

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