Interest Problem: “How many percent is 40 minutes less than 2.5 hours?”

[politexnik]

Good afternoon, I have problems with percentages, I can’t understand more precisely if, for example, the task says that: “How many percent is 40 minutes less than 2.5 hours?” correct would be ((2.5*60-40)*100)/40 or ((2.5*60-40)*100)/(2.5*60)? I don't need you to write the solution to this problem, I need to understand the percentage of which number I should calculate.

 

[stapel]

Good afternoon, I have problems with percentages, I can’t understand more precisely if, for example, the task says that: “How many percent is 40 minutes less than 2.5 hours?” correct would be ((2.5*60-40)*100)/40 or ((2.5*60-40)*100)/(2.5*60)? I don't need you to write the solution to this problem, I need to understand the percentage of which number I should calculate.

I'll scrape what was posted elsewhere for you:

You are looking at the 40 minutes (which equals 40/60 = 4/6 = 2/3 hours) in terms of the 2.5 hours. So 2.5 is the whole.

You are asked to find the difference between the two values (because 2.5 - 2/3 will give you the amount "less than"), and then to find the percentage of the whole that this difference represents.

So set up the standard "percent of" equation: (this) is (some percent) of (that). In your case, (this) is the difference and (that) is the whole. Of course, "is" means "equals" and "of" means "times".

Plug in your into, and solve.

 

[The Highlander]

Good afternoon, I have problems with percentages, I can’t understand more precisely if, for example, the task says that: “How many percent is 40 minutes less than 2.5 hours?” correct would be ((2.5*60-40)*100)/40 or ((2.5*60-40)*100)/(2.5*60)? I don't need you to write the solution to this problem, I need to understand the percentage of which number I should calculate.

Hi @politexnik,

The first thing you should do when comparing any two quantities is to ensure that they are both in the same units.
(So that you are not trying to "compare apples with oranges"! ?)

You should start, therefore, by converting the minutes to hours or the hours to minutes. Now, converting the minutes to hours involves dealing with a common fraction (⅔) or a recurring decimal fraction: 0.6666...
Therefore, although either approach will 'work', I would recommend converting the hours to minutes as being more convenient.

So, now you are comparing 40 minutes to 160 minutes (2½ hours), yes?

Consider these "comparisons"....
[math]\frac{40}{160} = \frac{4\cancel{0}}{16\cancel{0}} = \frac{4}{16} = \frac{1}{4} = 0.25~ (\equiv 25\%)[/math]and
[math]\frac{160-40}{160} = \frac{120}{160} = \frac{12\cancel{0}}{16\cancel{0}} = \frac{12}{16} = \frac{3}{4} = 0.75~ (\equiv 75\%)[/math]

*** So 40 minutes is what percentage of 2½ hours??? *** ?​

Does that illustrate how your second "calculation" ["((2.5*60-40)*100)/(2.5*60)"] is more relevant (to the original question) than your first attempt ["((2.5*60-40)*100)/40"] even though it doesn't actually answer what is asked of you? (See my question above, at: ***.)

Hope that helps. ?

 

[khansaheb]

160 minutes (2½ hours),

How's that?

 

[Dr.Peterson]

Good afternoon, I have problems with percentages, I can’t understand more precisely if, for example, the task says that: “How many percent is 40 minutes less than 2.5 hours?” correct would be ((2.5*60-40)*100)/40 or ((2.5*60-40)*100)/(2.5*60)? I don't need you to write the solution to this problem, I need to understand the percentage of which number I should calculate.

My difficulty with the problem is that the wording is very awkward! So I would start by trying to restate it in a way that is clearer, but is clearly equivalent:

How many percent is 40 minutes less than 2.5 hours?​

​

40 minutes is what percent less than 2.5 hours?​

This restatement puts it in the form

___ is ___% less than ___​

We might take it further:

The decrease from 2.5 hours to 40 minutes is what percent of 2.5 hours?​

Now, your work shows that you have, appropriately, converted to minutes, and taken the difference between 2.5 hours = 2.5*60 = 150 minutes and 40 minutes. You just want to know what to divide by.

My rewording should make it clear that the "base" or "whole" is the 2.5 hours, so your answer of ((2.5*60-40)*100)/(2.5*60) is the right one. (Now, of course, do it!)

On the other hand, I wouldn't write it out as one expression the way you have; but perhaps you did that just to show your thinking in a compact way.

 

[The Highlander]

How's that?

It's that because I was lured into the "neatness" of 160 minutes! Doh! ??

I have corrected the entire post, below...
(The original premise (converting to the same units) still stands but thank you for pointing out my error.)

Corrected version of Post #3...

Hi @politexnik,

The first thing you should do when comparing any two quantities is to ensure that they are both in the same units.
(So that you are not trying to "compare apples with oranges"! ?)

You should start, therefore, by converting the minutes to hours or the hours to minutes. Now, converting the minutes to hours involves dealing with a common fraction (⅔) or a recurring decimal fraction: 0.6666...
Therefore, although either approach will 'work', I would recommend converting the hours to minutes as being more convenient.

So, now you are comparing 40 minutes to 150 minutes (2½ hours), yes?

Consider these "comparisons"....
[math]\frac{40}{150} = \frac{4\cancel{0}}{15\cancel{0}} = \frac{4}{15} \approx 0.267~ (\equiv \scriptsize \text{(approx.)}~\normalsize 27\%)[/math]and
[math]\frac{150-40}{150} = \frac{110}{150} = \frac{11\cancel{0}}{15\cancel{0}} = \frac{11}{15} \approx 0.733~ (\equiv \scriptsize \text{(approx.)}~\normalsize 73\%)[/math]

(Note that 27% & 73% add to 100%)

*** So 40 minutes is what percentage of 2½ hours??? *** ?​

Does that illustrate how your second "calculation" ["((2.5*60-40)*100)/(2.5*60)"] is more relevant (to the original question) than your first attempt ["((2.5*60-40)*100)/40"] even though it doesn't actually answer what is asked of you? (See my question above, at: ***.)

Hope that helps. ?

 

[Dr.Peterson]

*** So 40 minutes is what percentage of 2½ hours??? *** ?

But that isn't what the problem asks for.

... your second "calculation" ["((2.5*60-40)*100)/(2.5*60)"] ... doesn't actually answer what is asked of you? (See my question above, at: ***.)

But it does.

Or are you interpreting the question,

“How many percent is 40 minutes less than 2.5 hours?”

differently than I do? It doesn't say "of".

Please explain.

 

[khansaheb]

Good afternoon, I have problems with percentages, I can’t understand more precisely if, for example, the task says that: “How many percent is 40 minutes less than 2.5 hours?” correct would be ((2.5*60-40)*100)/40 or ((2.5*60-40)*100)/(2.5*60)? I don't need you to write the solution to this problem, I need to understand the percentage of which number I should calculate.

This problem uses very similar concepts to that of your previous problem:

1. Text Task (Word Problems)​

   Bananas are 10% more expensive than oranges, and apples are 20% cheaper than bananas. 1. By what percentage is a banana more expensive than an apple? (Answer: 25%) 2. What percentage is the amount paid for 3 kg of bananas more than the amount paid for 2 kg of oranges? (Answer: 65%) 3. How...

Have you completed that problem?

 

[The Highlander]

Or are you interpreting the question differently than I do?

Please explain.

Yes, it would appear that my interpretation of the problem is different from yours.

I believe that what the question is asking is: what percentage reduction is there when a given time span, of 2½ hours, is reduced by 40 minutes.

Clearly, you think it means: what percentage of a given time span, of 2½ hours, remains if it reduced by 40 minutes. Yes?

I can see how your interpretation fits at least as well as mine but (in my opinion) the former interpretation is more likely to be what the original author(s) of the question intended to ask.

I don’t expect you (or many others in here) to agree with me on that but I would be grateful if you would at least admit the possibility that my interpretation might be correct?

Your own opening comment in this thread was: “My difficulty with the problem is that the wording is very awkward!”

I suspect that what we are faced with here may be translation into English perhaps losing some of the original meaning of the question? I very much doubt whether any native English speaker would phrase a question on percentage calculations the way this one has been worded.

Perhaps an ‘Admin’ can tell us where in the world the OP is located (based on their IP Address) to see if that is an English speaking country or whether it is likely that the OP’s problems are being translated (either by the OP or some engine like Google’s) into English before being posted here? (@stapel ?)

Unfortunately, this OP does not have a good record of responding to requests made of her/him by forum members about how s/he has progressed in answering the problems posted. We have yet to see worked answers to anything posted by the OP or, indeed, any responses to questions put to her/him (other than one admission that s/he had misnamed a triangle as equilateral when it was actually isosceles).

In the thread to which @khansaheb refers (Text Task (Word Problems), qv) the OP requested help with four questions to which answers were also included. However, it was simply not possible to answer two of those questions (Nos. 2 & 3) without further information or making a (very unlikely) assumption (that every banana and every orange and every apple all share the same individual mass!). Now if that was a “given” by the question setter(s) or the student was advised to make that outlandish assumption, then that information was not shared with us.

Perhaps there was also further information provided with this problem that would have made it clear how to correctly interpret the question as worded.

Notwithstanding this OP’s apparent reluctance to respond to individual requests I will (in subsequent posts) ask for further information about this problem as (once again, in my opinion) that is the only way we are likely to get a definitive answer on how to interpret the original question correctly. ?

 

[The Highlander]

Good afternoon, I have problems with percentages, I can’t understand more precisely if, for example, the task says that: “How many percent is 40 minutes less than 2.5 hours?” correct would be ((2.5*60-40)*100)/40 or ((2.5*60-40)*100)/(2.5*60)? I don't need you to write the solution to this problem, I need to understand the percentage of which number I should calculate.

@politexnik

Do you have an answer that came with this problem?

If so, please tell us what answer was provided to you as the correct solution.

Thank you.

 

[The Highlander]

Good afternoon, I have problems with percentages, I can’t understand more precisely if, for example, the task says that: “How many percent is 40 minutes less than 2.5 hours?” correct would be ((2.5*60-40)*100)/40 or ((2.5*60-40)*100)/(2.5*60)? I don't need you to write the solution to this problem, I need to understand the percentage of which number I should calculate.

@politexnik

Has this problem been translated into English from your own language?

If so, please provide us with the problem as it appeared in its original form.

A picture or text, either would be fine, but if there is any other (surrounding) text or information that accompanied the problem that would be useful too.

For example, is there an opening 'story' that describes the situation or context in which the problem is set?

Or are there any questions before this one that are based on the same or similar situation?

Thank you.

 

[Dr.Peterson]

Yes, it would appear that my interpretation of the problem is different from yours.

I believe that what the question is asking is: what percentage reduction is there when a given time span, of 2½ hours, is reduced by 40 minutes.

Clearly, you think it means: what percentage of a given time span, of 2½ hours, remains if it reduced by 40 minutes. Yes?

No, my interpretation is that the time is reduced to 40 minutes, not by 40 minutes:

My difficulty with the problem is that the wording is very awkward! So I would start by trying to restate it in a way that is clearer, but is clearly equivalent:

How many percent is 40 minutes less than 2.5 hours?​

​

40 minutes is what percent less than 2.5 hours?​

This restatement puts it in the form

___ is ___% less than ___​

We might take it further:

The decrease from 2.5 hours to 40 minutes is what percent of 2.5 hours?​

I imagine that you are thinking of it as something like this (which was possibly my first thought when I read it):

If we subtract 40 minutes from 2.5 hours, what percent is ... that reduction?​

I rejected that because it is too big a restructuring; it makes more sense, if you must make that sort of change, to take it as

If we subtract 40 minutes from 2.5 hours, what percent is ... that (the result)?​

When I restate a question, I like to move words around minimally (sometimes one step at a time) and make sure I haven't changed the meaning. In this case, because the word order is so nonstandard, one can argue that what I did, small as it is, did change the meaning (though I don't think so).

But you are right that the awkward English suggests that this question (and the others) could be either a poor translation into English, or the result of an author using a non-standard dialect (or simply not knowing English well, and translating from their native language.)

I do find it interesting that the wording of this matches part of the other set. I haven't looked at those in detail; I will now go to that thread and try restating them to see what I think of them.

 

[Steven G]

Hi @politexnik,

The first thing you should do when comparing any two quantities is to ensure that they are both in the same units.
(So that you are not trying to "compare apples with oranges"! ?)

You should start, therefore, by converting the minutes to hours or the hours to minutes. Now, converting the minutes to hours involves dealing with a common fraction (⅔) or a recurring decimal fraction: 0.6666...
Therefore, although either approach will 'work', I would recommend converting the hours to minutes as being more convenient.

So, now you are comparing 40 minutes to 160 minutes (2½ hours), yes?

Consider these "comparisons"....
[math]\frac{40}{160} = \frac{4\cancel{0}}{16\cancel{0}} = \frac{4}{16} = \frac{1}{4} = 0.25~ (\equiv 25\%)[/math]and
[math]\frac{160-40}{160} = \frac{120}{160} = \frac{12\cancel{0}}{16\cancel{0}} = \frac{12}{16} = \frac{3}{4} = 0.75~ (\equiv 75\%)[/math]

*** So 40 minutes is what percentage of 2½ hours??? *** ?​

Does that illustrate how your second "calculation" ["((2.5*60-40)*100)/(2.5*60)"] is more relevant (to the original question) than your first attempt ["((2.5*60-40)*100)/40"] even though it doesn't actually answer what is asked of you? (See my question above, at: ***.)

Hope that helps. ?

Yesterday I compared oranges and apples and found that apples are larger. Does that help?
Math keeps getting harder. I was finally understanding a little about x's and y's and now there is apples and oranges!

 

[khansaheb]

Yesterday I compared oranges and apples and found that apples are larger. Does that help?
Math keeps getting harder. I was finally understanding a little about x's and y's and now there is apples and oranges!

Just wait till Watermelons and Pineapples and Blueberries come into play ????