Find the loss or gain percent on the total cost price.

[chijioke]

A garage owner sells two cars for N300 000.00 thereby making profit of 20 percent on the cost price of the first and a loss of 20 percent on the cost price of the second. Find the loss or gain percent on the cost price.

This is my attempt in solving the problem.
Let the cost price, C.p on the first car be m.
Let the cost price, C.p on the second car be n.
Then the selling price, S.p on the first car is $$\frac{120}{100}~m$$Selling price, S.p on the second car is $$\frac{80}{100}~n$$S.p for the two cars is $$\frac{120}{100}~m~ + \frac{80}{100}~n~ = N 300 000$$$$\frac{12}{10}~m~ + \frac{8}{10}~n~ = N 300 000$$$$12m + 8n = N 3000 000.00$$How can I go further now?

 

[The Highlander]

A garage owner sells two cars for N300 000.00 thereby making profit of 20 percent on the cost price of the first and a loss of 20 percent on the cost price of the second. Find the loss or gain percent on the cost price.

How can I go further now?

Hi @chijioke,

I'm afraid there's nothing much further you can do from where you've gone.

You have two variables and only one equation!

I'm not entirely sure I understand what this question is asking (perhaps something has been 'lost in translation'?).

However, I am working on a little exercise that may shed some light on how to arrive at a possible answer; give me a few minutes and I will get back to you with what I've produced.

 

[The Highlander]

@chijioke

The way this question has been presented, I'm not terribly sure I know what it is asking you to do.

The only thing I can think of is that they want you to say how the profit made varies when the cost prices of the two cars vary.

I have set up a little spreadsheet that illustrates this and a picture of the results is shown below (qv).

In my spreadsheet, CP stands for Cost Price, SP stands for Selling Price and Car A is the one the dealer makes the 20% profit on (Car B, therefore, is the one with the 20% loss).

Points to note:-​

1. The highest price that Car A can be is N250 000 because Car B then has a zero Cost Price and the net profit is then just the 20% made on Car A but that's an unlikely scenario (since Car B probably cannot have zero cost price?) So the Maximum profit is ≤ 20% (though, as I say, 20% is unrealistic).​

​

2. The profit reduces as the cost price of Car A drops below N250 000.​

​

3. Until the cost price of both cars is N150 000 (ie: the same) then there is zero profit made.​

​

4. Once the cost price of Car A is below N150 000, then the profit becomes negative, ie: there is a net loss​

​

5. The maximum loss (-20%) occurs when Car A has zero cost price but, again, this is an unlikely scenario.​

All I can think of is that the question expects you to produce a formula (in terms of your m & n?) that will quantify this relationship (between the cost prices of the two cars and the net profit realized as those prices vary).

Do you think you could do that?

Have a go and let us see your attempt then further advice will be offered if necessary.

Hope that helps.

Spreadsheet Output:-



PS: I have attached my spreadsheet ("# Car Sales.txt") so that you can download it and play around with it if you wish but, if you do download it, you must immediately change its filename from "# Car Sales.txt" to "# Car Sales.xlsx" so that it may be opened as a spreadsheet.

 

[chijioke]

@chijioke

The way this question has been presented, I'm not terribly sure I know what it is asking you to do.

The only thing I can think of is that they want you to say how the profit made varies when the cost prices of the two cars vary.

I have set up a little spreadsheet that illustrates this and a picture of the results is shown below (qv).

In my spreadsheet, CP stands for Cost Price, SP stands for Selling Price and Car A is the one the dealer makes the 20% profit on (Car B, therefore, is the one with the 20% loss).

Points to note:-​

1. The highest price that Car A can be is N250 000 because Car B then has a zero Cost Price and the net profit is then just the 20% made on Car A but that's an unlikely scenario (since Car B probably cannot have zero cost price?) So the Maximum profit is ≤ 20% (though, as I say, 20% is unrealistic).​

​

2. The profit reduces as the cost price of Car A drops below N250 000.​

​

3. Until the cost price of both cars is N150 000 (ie: the same) then there is zero profit made.​

​

4. Once the cost price of Car A is below N150 000, then the profit becomes negative, ie: there is a net loss​

​

5. The maximum loss (-20%) occurs when Car A has zero cost price but, again, this is an unlikely scenario.​

All I can think of is that the question expects you to produce a formula (in terms of your m & n?) that will quantify this relationship (between the cost prices of the two cars and the net profit realized as those prices vary).

Do you think you could do that?

Have a go and let us see your attempt then further advice will be offered if necessary.

Hope that helps.

Spreadsheet Output:-

View attachment 37848

PS: I have attached my spreadsheet ("# Car Sales.txt") so that you can download it and play around with it if you wish but, if you do download it, you must immediately change its filename from "# Car Sales.txt" to "# Car Sales.xlsx" so that it may be opened as a spreadsheet.

Thank you for your interest in assisting me do my homework. I changed the file name as instructed. Yet I could not access it because it could not open.

 

[The Highlander]

Thank you for your interest in assisting me do my homework. I changed the file name as instructed. Yet I could not access it because it could not open.

Please check that the filename has been changed to:-

# Car Sales.xlsx​

The filename must look exactly like that (or, at least, the bit after the full stop must be: xlsx or XLSX) for the file to Open as a spreadsheet. You haven't changed it to x1sx (using the number 1 instead of the letter l (ie: a lower case L) have you?

Please look at what you have changed it to again. (I just downloaded the attachment and, after changing the filename to: # Car Sales.xlsx, it opened fine in Excel here.)

[You could just Copy what is inside the quotation marks (in red) here: "# Car Sales.xlsx" and then Paste that into your filename. ]

If you get an error message telling you that the file cannot be opened because it is not a "valid" Excel file or is possibly "corrupt", then try downloading it again and start over from there.

Do you have the Microsoft Excel™ program installed on your computer? If you don't have that installed (or a similar program that can open Excel spreadsheets) that would explain the problem.

There are plenty of alternative (free) programs available that can Open Excel spreadsheets; have a look here.

Or, if you have (or are willing to create) a Microsoft account, then you can use Microsoft 365 for free on the web.

However, you don't really need to be able to access the spreadsheet. The information I provided in my post above should be sufficient for you to approach the question on the basis I suggested (unless anyone thinks that what I suggested is the wrong approach?).

Can you not have a go at creating a formula that would do what I suggested without opening the spreadsheet?

 

[Dr.Peterson]

A garage owner sells two cars for N300 000.00 thereby making profit of 20 percent on the cost price of the first and a loss of 20 percent on the cost price of the second. Find the loss or gain percent on the cost price.

What you've done, it seems to me, is all that can be done with the problem as shown.

Rather than try making spreadsheets or formulas, I'd want to figure out what the problem actually intends. I'd start by making sure you copied it completely and exactly; is there additional information in the context that you didn't notice? Could you provide an image of the original? And, in the title the word "total" has been inserted; did you omit that in the problem itself? (It makes the problem clearer.)

There are various additional assumptions one might make, such as that the two cars are identical, with the same cost price (m=n), or that they both are sold at the same price. But neither is stated or implied. In fact, one possibility is that the intended answer is "There is not enough information," and they want to trip up people who make an unjustified assumption (e.g. just adding +20% and -20% to get an answer of 0).

It's also possible, of course, that this is simply a defective problem; can you ask the author, or is there reason to distrust them?

But I have to say that the work you did is very good.

 

[chijioke]

But I have to say that the work you did is very good.

Thank you.

Could you provide an image of the original?

 

[The Highlander]

Thank you.

View attachment 37870

Thank you for posting that.

So the problem is just exactly as you first posted it.
(Are there no Answers supplied with these problems?)

I can inly reiterate, therefore, that, in the absence of any clearer aim, I can only deduce that you are expected to create a formula or expression that gives the percentage profit or loss that will be obtained based on the cost price of one (or both) of the cars.

That is possible (though a bit messy) and I would imagine it would have to have certain condition(s) attached to it like variable ranges, eg: if you assign the letter m to the cost price of the car that makes a 20% profit then you would need to add a range for it to your formula like (0 < m < ₦250 000).

If you have a go at coming up with a formula I will offer my opinion.

PS: Did you have any luck opening my spreadsheet? (Not that you need it to work on this problem, it was just something I put together quickly to illustrate how the net profit was linked to the cars' prices).

PS:

 

[chijioke]

You haven't changed it to x1sx (using the number 1 instead of the letter l (ie: a lower case L) have you?

Yes. I changed it. In fact I copied and pasted it as you presented into the file name. At first it tried opening and later could not.

If you get an error message telling you that the file cannot be opened because it is not a "valid" Excel file or is possibly "corrupt", then try downloading it again and start over from there.

For the fact that I tried at first and it didn't open (even when I copied and pasted the text as you wrote it), I just lost interest in it. Though as I acknowledged at first, I really appreciate the effort you put in seeing that I am assisted.

PS: Did you have any luck opening my spreadsheet? (Not that you need it to work on this problem, it was just something I put together quickly to illustrate how the net profit was linked to the cars' prices).

It refused to open in my computer. As I had told you earlier, I am no longer interested in the problem. Don't bother. Maybe the wording of the problem is not well framed or some more information is needed in solving the problem. Don't you think so.

(Are there no Answers supplied with these problems?)

The answer supplied for the problem is 4% . I don't know what they mean by that.

 

[The Highlander]

The answer supplied for the problem is 4% . I don't know what they mean by that.

It's very interesting to know that you had an answer for this.

Do you have answers for all the questions that you post?
And are you only posting those questions where you don't get the same answer as your book?

If you have an answer for any problem you post, then you should post that answer with your question. That can be a great help to us because we can often work backwards from an answer to check how a problem is meant to be solved.

For example, in this case, is the answer a 4% LOSS?

If the answer is a 4% Loss then I can think of a way to get that answer.

You posted a picture of the question so we know that you posted it correctly but re-reading it now (in light of the answer you have given us) I think there may be a way to interpret the question that would lead to a 4% loss being the correct answer.

The question would still be very badly worded but if it meant that the dealer sold the cars for ₦300 000 each then the dealer would make a 4% loss on the sale of these cars!

Car A is sold for ₦300 000 but with a 20% profit which means the cost price of Car A was: ₦250 000 (20% of ₦250 000 is ₦50 000 and ₦250 000 + ₦50 000 = ₦300 000; the price it was sold for).

Car B is also sold for ₦300 000 but at a 20% loss which means the cost price of Car B was ₦375 000 (20% of ₦375 000 is ₦75 000 and ₦375 000 - ₦75 000 = ₦300 000; the price it was sold for)

Therefore, the total cost price of both cars was ₦625 000 (₦250 000 + ₦375 000) but he only got ₦600 000 for both of them when he sold them which means he made a ₦25 000 LOSS on the deal. (₦625 000 - ₦600 000 = ₦25 000).

And ₦25 000 is 4% of ₦625 000. $\displaystyle \left(\frac{25000}{625000}=0.04\text{ and }0.04\times 100\% = 4\%\right)$

So the dealer did make a net 4% loss on these sales.

I trust that clears up that one (even though you've lost interest in it )

 

[chijioke]

Do you have answers for all the questions that you post?

Yes I do in most cases.

And are you only posting those questions where you don't get the same answer as your book?

Exactly!

If you have an answer for any problem you post, then you should post that answer with your question.

Okay. I will.

That can be a great help to us because we can often work backwards from an answer to check how a problem is meant to be solved.

Okay.

For example, in this case, is the answer a 4% LOSS?

They did not specify whether the 4% is gain or a loss. The only thing there is just 4%.

I think there may be a way to interpret the question that would lead to a 4% loss being the correct answer.

Unless you think so otherwise. It was not stated whether the 4% is a loss or profit.

but if it meant that the dealer sold the cars for ₦300 000 each then the dealer would make a 4% loss on the sale of these cars!

That is the problem. If it had stated that the selling price of each car is N300, 000. I may not have any need of coming to the forum. I may have solved the problem since.

Car A is sold for ₦300 000 but with a 20% profit which means the cost price of Car A was: ₦250 000 (20% of ₦250 000 is ₦50 000 and ₦250 000 + ₦50 000 = ₦300 000; the price it was sold for).

Car B is also sold for ₦300 000 but at a 20% loss which means the cost price of Car B was ₦375 000 (20% of ₦375 000 is ₦75 000 and ₦375 000 - ₦75 000 = ₦300 000; the price it was sold for)

Therefore, the total cost price of both cars was ₦625 000 (₦250 000 + ₦375 000) but he only got ₦600 000 for both of them when he sold them which means he made a ₦25 000 LOSS on the deal. (₦625 000 - ₦600 000 = ₦25 000).

And ₦25 000 is 4% of ₦625 000. (25000625000=0.04 and 0.04×100%=4%)\displaystyle \left(\frac{25000}{625000}=0.04\text{ and }0.04\times 100\% = 4\%\right)(62500025000=0.04 and 0.04×100%=4%)

So the dealer did make a net 4% loss on these sales.

I trust that clears up that one (even though you've lost interest in it

I think I have to agree with you that the selling price of each car is N300 ,000 instead of the total selling price of both cars to be N300, 000, if the solution must be 4% loss.
Because I don't think or know any other way to interpret the problem to make the answer 4% profit. Or is there any?

 

[The Highlander]

I think I have to agree with you that the selling price of each car is N300 ,000 instead of the total selling price of both cars to be N300, 000, if the solution must be 4% loss.
Because I don't think or know any other way to interpret the problem to make the answer 4% profit. Or is there any?

Good, I'm very glad that you "agree" with me.
Well, I can't think of any (and I dare anyone else to come up with one! )

Now that you have confirmed that you do have answers available (to most, if not all, of these problems) and you are only posting those where the answer you get differs from the one in your book(s), please now post the published answer to the problem you have posted in this thread (so that we can properly check your working there).

Regards,
TH