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Finding profit percent

Let's find profit percentage using a couple of examples that have simple numbers. Created by Aanand Srinivas.

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Video transcript

so in this video let's see how to calculate the profit percentage to do that let's start with the problem maybe you bought something you you buy something for tender piece and let's say you sold it you sold it for 12 now the question asks us can you find the profit can you find the profit and also can you find the profit profit percentage profit I'm gonna use this sign for percentage can you find these two things now I want you to pause the video and see if you can now find the answer to both of these and it's let's check if the both of us did it the same way now the first part is quite simple I'm just going to say okay I bought for 10 the way I read this question is bought for 10 oh that's another way of saying my cost price equals 10 and now I sold for 12 and that's just another way of saying my selling price equals 12 and I know that my profit is simply the difference between these two so I know that my profit P rof I did my profit equals 12 minus 10 which is 2 rupees so that's my profit but now the interesting question here is what's the profit per sentence now before we jump into this I want to do a quick refresh a quick reminder of what percentage means per centage percent I'm writing it separately so that we notice this percent over here person simply means for every hundred for every hundred or per hundred cent from century and centimeter you know that always has something to do with 100 in it so in general what is the percentage mean let me just bring it all up over here so percent in general means per hundred so a simple way to say what a percent is is the numerator it's a numerator of a fraction whose denominator is hundred numerator of a fraction whose denominator whose denominator is hundred I know it's a big way to say it is 100 but this big sentence in the language of math is simply by hundred something by hundred if this is 30 by hundred then we say this is 30 per sentence these two sentences are the same thing 30 out of 130 percentage are exactly the same things just do different ways to say the same thing and you probably know this but I'm just using a refresh that we can now look at what profit percentage means so this has been fifteen by hundred that's another way of saying fifteen percent in fact this number can be more than hundred it doesn't always have to be less than hundred I can have 120 by 100 and what is that equal to that's 120 percentage now let's get to the question over here which is not just the percent but what's the profit percent so let's let's do that over here so the question wants you to find out the profit percentage I'm gonna write this out like this profit per 100 cause price that's what this sentence actually means so when we say calc can you calculate profit percentage when your cost price was what was it again it was ten and your selling price was twelve when it's asking you can you find profit percentage what you're really being asked is can you find the profit per hundred cause price another way to say the same thing is profit for a cost price of hundred cause price 100 and this will become more clear with an example so cos price was ten how much did you make two rupees and now what is it asking this question is asking what profit would you have made if your cos place 100 rupees so you bought for 10 rupees let's write the cost price over here you bought for 10 and you made 2 rupees so profit is 2 rupees what if you had bought for a hundred then how much would your profit have been if you calculate this answer this is what we call profit percentage and now there are many ways to get to this answer now one way that I think about it is for you give me you gave me 10 rupees I made two rupees profit if you give me 100 rupees how much will I make so this is very similar to asking the question 10 bananas cos 2 rupees then how much 100 bananas cost we have solved many problems like this so in my mind I'm just going okay 10 times 10 gives me 100 then 2 times 10 will give me what because I know how to multiply by 10 to go from 10 200 so then I must multiply to the same thing to get to the answer over here and so what is that ons are gonna be 2 times 10 is 20 so 20% is the answer to this question that we have so for 10 rupees costs price I made a 2 rupee profit so for a hundred rupee cost price I'll make up 20 rupees profit or in other words I have a 20% profit now notice that this is not a new thing you're learning another way to look at the same thing is as a fraction problem so this is the same thing as asking you made 2 rupees for 10 rupees how much will you make how much will you make for 100 rupees now isn't this just a fraction problem where three things are given and you have to find this thing over here there are many ways to do it we just did it in one way by asking to go from here to here 10 has been multiplied by 10 so if this fraction has to be equal you have to multiply this also by 10 and that's what we did we wrote 20 by 100 so the question is asking you convert this fraction to a fraction whose denominator is 100 and you'll notice that you don't need any formula to do this one of the problems that I see is that students tend to think that profit and loss has some formulas and then simple interest has other formulas discount has other formulas but you start seeing that all of these are the same problem let's look at one more problem to see that maybe this time the cost price is thousand so you're buying a big thing now and then you're selling it your selling price is thousand fifty so how much profit did you make here now the profit you made is fifty rupees thousand fifty minus thousand so he made a 50 rupee profit bigger than what the previous person made he just made a 2 rupee profit but let's see what the profit percentages profit percentage what is that going to be now you know everything you need to know to calculate the answer to this question so pause the video and look at what answer you get and let's let's think this through together so you've thought and you have an answer with you let's do this together the way I'm doing it in my head is I'm going okay so the cost price was thousand the cost price was thousand and the profit I made was fifty and when somebody's asking me what profit percentages in my head I am breaking this down into oh you want profit percentage in other words you want how much profit would I have made if my cost price had just been 100 and now I look at this and I go okay thousand rupees I made fifty profit four hundred rupees how much would I have made I know to go from thousand two hundred I have to divide by ten or in other words multiplied with one by ten thousand by 10 gives me hundred so to keep the whole thing equal I have to multiply this also by one by ten and what will I get over here 50 times 1 by 10 1 by 10 or in other words five percent 50 by 10 five percent so the profit percentage here here is five percent and once again I want you to notice that this is nothing different you've just been asked this fraction question 50 by thousand equals how much by one hundred how much by one hundred profit by cost price equals how much by one hundred and this what we have over here is what we call our profit percentage I'm gonna write profit percentage and that's what you did you did this in this way by taking thousand divided by ten in other words into 1 by 10 and 50 into 1 by 10