Download Subtitles for Percentages 1: Fractions to Percentages – CAT 2026 Arithmetic by Ravi Prakash Rodha

[Music] [Music] hi everyone my name is ravi prakash and welcome to first class of percentages percentage is super important topic every line i say every question i solve so important in this percentage topic right because this will build up your foundation to solve all the arithmetic problems all the calculations all the data interpretation sets right everywhere this percentage will help okay i have to be very good at percentages solving percentages i hope you have watched speed man we have watched those speed match videos where we discussed how to do fast calculation in percentages right so all those things very important percentages okay so before percentages please watch those uh speed match videos right further boost up your confidence in percentages okay so let's start percentages one first class of percentages right now see here first we will see all the fraction fraction to percentage conversion we should remember it right fraction to percent is conversion like start starting from one by one obviously one by one is what one by one is hundred percent right one by two what is one by two fifty percent we should remember to 1 by 19 okay what is 1 by 3 33.33 percent right what i'm doing actually is any fraction any fraction multiplied by 100 will give me the percentage value right so half into hundred is what fifty so fifty percent okay one by three into hundred so it is hundred by three what is hundred by three thirty three point three three so when you multiply any fraction by percent a hundred it becomes percentage right because what is percentage means percentages means per 100 percentages means per 100 okay percent per cent percent sentiments sent means 100 okay so percent the sentence in century word also century century contains cent right so sent means hundred century means hundred okay so again so do all this right now one by four you can calculate you can remember easily also right what is one by four one by four into hundred is what one by four into hundred twenty five percent okay one by five and two hundred is what twenty percent okay now one by six now you can connect this now you can connect it now what is one by six here you see one by three half is one by six so what is thirty three point three three half sixteen point six six percent correct now what is one by seven so what is one by seven so again now seven you can't connect with the previous one because one by seven it is right one by seven when you multiply it by hundred it becomes hundred by seven so i know seven fourteen ja ninety eight and 2 is left so 14 plus 2 by 7 is written by 14 2 by 7 but in decimal right so 1 by 7 is approximately 0.14 1 by 7 is approximately 0.14 so 2 by 7 is approximately 0.28 you can remember it 14.28 percentage okay one by seven fourteen point two eight percent easy to remember also because seven two fourteen fourteen two twenty eight so it's easy to remember then one by eight one by eight is what it is half of one by four what is one by four twelve four twenty five percent what is half of twenty five twelve point five percent one by nine again nine is not a prime number you can easily connect with any previous one 1 by 9 is what 1 by 9 is one third of one one by three one by nine is one third of one by three what is one by three thirty three point three three it's one third how much eleven point one one percent okay one by ten is obviously ten percent which i should not write this okay one by ten is ten percent one by ten multiplied by hundred ten percent one by eleven again you solve like this one by eleven into hundred so see 1 by 11 into 100 let me write here each step is so important right how to calculate being making calculation here your calculation making fast okay 1 by 11 in 200 ninety nine so nine plus one by eleven is left this is nine one by eleven in which fraction and which fraction is plus sign is hidden okay nine one by eleven so nine one by eleven is what what is one by eleven one by eleven is approximately point zero nine so it is how much it is nine point zero nine percent is okay now one by twelve so how much one by twelve one by nine twelve is not a prime number and we can connect with another any previous one value so one by twelve is half of one by six what is one by six sixteen point six six percent okay half of sixteen point six six percent eight point three three percent what is one by thirteen one by thirty is what seven point seven percent okay seven point seven percent remember it one by thirteen is seven point seven percent seven point six nine to be exact but you can remember seven point seven so one by fourteen what is 1 by 14 half of 1 by 7 14.28 half is how much 7.14 percent you remember this value right remember is so important till 1 by 19. now 1 by 15. now what is 1 by 15 it is one third of 1 by 5. it is one third of one by five what is one by five twenty percent one third of twenty percent how much six point six six percent okay twenty by three is six point six six one by sixteen what is one by sixteen it is half of one by eight what is one by eight twelve point five twelve point five half is how much six point two five percent okay one by seventeen what is one by seventeen so again remember here one by seventeen is five point eight eight right you can sense this value actually so one by this kind of value values right when it gets tougher now or one by 17 and all so 1 by 17 into 100 if you multiply so 1 by 17 into 100 how much it is so 17 6 java 1 0 2 so it is just slightly less than 6 slightly less than 6 right because 17 into 6 is 1 0 slightly less than 6 5.8 percent this kind of approximation you can do okay now 1 by 18 1 by 18 it is 1 by 18 it is half of 9.09 sorry it is half of 1 by 9 what is half of 1 by what is one by nine eleven point one one what is half of eleven point one one so eleven point one half is what five point five five what is one by nineteen so one minute is what it is five we remember five point two six percent see i'll discuss one by nineteen also this approximations you should understand one by nineteen when multiplied by hundred it becomes nineteen five ninety five 5 is left because it is 100 here 5 plus 5 by 19. now what is value of 5 by 19 so had it been 5 by 20 so 5 by 20 was exactly 1 by 4 what is 1 by 4.25 right had it been had it been had it been five by twenty so five by twenty is exactly one by four that is point two five but it is five by nineteen so five by deliver then five by twenty is slightly more because derivative is less so fraction is slightly more so 0.25 slightly more right so we're right here 0.26 that's why okay so what is one by 19 around 5.26 percent right this kind of approximations you can make very important this data very important okay because this is only the unique table right now we can again derive very values from here and many questions we can frame from here okay so very important data right okay now you should apply this kind of funda you should apply this kind of funda right when we when you say suppose i want to calculate value of 1 by 23 okay so what is 1 by 23 now so again you multiply by 100 23 into 4 is 92 8 is left 8 by 23 so again you can sense here okay if it was 8 by 24 perfectly 1 by 3 that is 0.33 but it is 8 by 23 here that means little bit more than 8 by 24 that means little bit more than 0.33 so you can rewrite it as 4.34 slight less than point slight more than 0.33.34 so it is 1 by 234.34 percent to the right this kind of approximation you should understand you should understand this kind of approximations okay i hope it is clear this part okay now come to next part here so how to uh derive values from the table right suppose now i'm writing all those important values which are used throughout the quant okay we will find these numbers throughout the quant every time okay and it will be useful table only so i hope you've written table in the notebook okay so see 12 suppose i need to find the value of what is the 37.5 percentage of okay of 640 so this is our table are you right 37.5 percent special number itself right so again what is what is the series now you see 37.5 so you see some you see some 0.5 in this series right you search for some point five percent test you will see that one by eight is twelve point five percentage right there's a whole series you should remember just twelve point five series i say twelve point five then the next number is three by eight that is thirty seven point five percent because twelve point one by eight multiplied by three so twelve point five multiplied by three thirty seven point five then five by eight okay let me write it here okay because very important date i am writing here okay so since 1 by 8 is 12.5 percent that means 3 by 8 is point 37.5 percent okay what is five by eight plus twelve point five into five that is sixty two point five percent it is seven by eight twelve point five into seven that is 87.5 this value should values you should remember okay so if you remember things will become very easy 37.5 percent that means three by eight three by eight of 640. you cancel it it it 80 times what is 18 to 3 240 right so it becomes so easy to calculate value of 37.5 percent of 640 very easy to calculate the value okay now suppose 18.75 percent of eighteen point seven five percent of 176 right now looks like a tough question looks like a tough question is actually not again if you get defunder from where does 18.75 percent comes right you directly see from here on itself okay that is it is eighteen point seven five is the half of thirty seven point five right thirty seven point five half is eighteen point seven five what is it 39.5 three by eight what is 18.75 percent half of 3 by 8 that is 3 by 60 so if you get 3 by 16 so you can now sense it okay 1 by 16 was 6.25 percent so from here also i can connect y 1 by 16 was 6.5 because 1 by 8 was 12.5 half of it so 1 by 16 6.25 6.25 into 3 6.25 into 3 is 18.75 percent right into three so that means it is three by sixteen so it becomes very easy job becomes very easy right three by sixteen into one seventy six you can cancel here eleven times what is the answer answer is thirty three such a beautiful uh numbers these are right to directly get the fraction value and just solve it okay so got to be familiar with this kind of numbers okay 37.5 18.75 all the numbers i will write right one by one okay see how many numbers have covered here so many numbers 87.5 62.5 37.5 18.75 other than the table right so this is a very important concept okay now 83.33 of of uh 83.33 percent off now let's take any number take 606. again looks like a tough question but it is not what is eighty three point three three fifteen gonna connect right many ways to connect eight three point three three if you remember one by twelve is eight point three three percent this is ten eighty three point is 10 times of 8.33 right 10 times 1 by 12 10 times so 10 by 12 10 by 12 is 83.33 percent can cancel 10 by 12 how much it is 5 by 6 5 by 6 therefore five by six is eighty three point three three percent one more thing you can do right again two is just break this right eighty three point three three percent so problem is due to this decimal part right 0.33 so see in in the table in table where does 0.33 come in decimal parts you can see it 33.33 okay so you can break this as you can break this as 50 plus 33.33 percent okay fifty percent plus thirty three point three three percent what is fifty percent one by two what is this one thirty percent one by three one by two plus one by three how much five by 6 that is 1 by 2 plus 1 by 3 is what it is 5 by 6 so 5 by 6 right so 5 by 6 is 83.33 percent okay 5 by 6 is 83.33 what is the answer here so this value is ultimately right either you go by 1 by 12 way or you go by just breaking by breaking this numbers right what is the value of 83.33 percent five by six remain remember it very important value 83.33 you will see lots of time this because this kind of numbers in percentage and and quantity so 5 by 6 of 606 in cancel 1 0 1 times so 1 0 1 into 5 is what 5 0 5 so 5 0 5 is the answer right so all these some very nice numbers we are discussing okay next one next one 43.75 off right 43.75 percent of 352. now what is this 43.75 percent again if you see here you can solve this like 43.75 okay it is like 50 percent minus 6.25 percent you can break like this 50 percent is 1 by 2 6.25 is 1 by 16 okay so this is how much this is 7 by 16. okay one similar number is 56.25 percent okay so it is 50 plus 6.25 percent that is 1 by 2 plus 1 by 16 that is 9 by 16 so two important numbers here right 43.75 and 56.25 percent right these numbers you'll see by solving questions further in quant okay so remember these values 7 by 16 9 by 16 okay so you can simply solve it now this is how much this is 7 by 16 into 352 resolve it now 16 to the 32 and 2 22 into 7 20 to 7 142 into 7 14 140 plus 14 154 so this is the answer right so all these numbers you got to remember okay now next thing we'll discuss next thing next thing will be multiplying factor okay multiplying factor in percentages okay what is multiplying factor you see see all these concepts we are doing and doing small small problems but very important problems right whole percentage will be used in throughout in profit and loss sici whole arithmetic mixtures okay time and distance time and work everywhere some question numbers also right everywhere data interpretation everywhere percentage is there so for sentence you understand thoroughly every line you will listen and you solve these questions right we'll be doing lots of good good coverage of questions good variety of questions in this okay but what is multiplying factor right multiplying factor as a name suggests by what factor i should multiply okay by what factor should we multiply this is the meaning of multiplying factor right multiplying factor so see here suppose a number here is see it will be used it is very useful in this kind of question suppose i give you a question 840 is a number right you have to decrease 87.5 percent decrease what is the value okay so in this kind of question it is very useful right it's doing multiplying factor so it is basically one step up one step up right one step up miss while solving we can do that one step in mind and directly can write and get the answer it will be faster if you understand this right see what is multiplying factor now so if i solve for it is n point five percent okay so let's say a number is x let's say a number is x i am decreasing 20 percent on x what is this result can write result as okay x minus 20 percent of x is what you'll write normally x minus 1 by 5 of x okay this becomes x into 4 by 5 right and talking about this x into 4 by 5 this is what i'm talking about my multiplying factor sorry my multiplying factor right x to be decreased by 20 by what factor i should multiply 4 by 5 this is the multiplying factor right similarly here also x is decreased by 87.5 percent x is decreased by it is n point 5 percent by what factor i should multiply so what is that 7.5 percent seven by eight so x minus seven by eight of x i can write the discussion last flight right it is n point five percent is what uh uh seven by eight twelve point five percent one by eight it's in point five percent seven by eight so the result result is x into one by eight this is my multiplying factor this is my multiplying factor right by what the factor i should multiply to get the result so x being decreased by design point five percent simply multiply by 1 by 8 so what is the answer here 840 decrease by 87.5 percent simply multiply by one by eight so eight eight sixty four so answer is what answer is eighty sorry not editor 64 i'm sorry is 840 yeah okay so it is one zero five so one zero five is the answer okay so how to get this quickly okay they get this funda in mind multiplying factor is formed by when you when you do the operation when you do the operation with fractions in a question right suppose this question so x minus twenty percent of x so x minus one by five of x right so i've done the all the operation here x minus 1 by 5 of x what is 1 x into what is x you get a common so once you take x as common when you break this step you take x as common it becomes 1 minus 1 by 5 right so always this x will become as common and this is always one here also right here also taken i have skipped this step but what is it what if i write this step here this step will look like x you take common here so if you take x some common 1 minus 7 by 8 okay 1 minus 7 by 8 right so this is 1 minus 7 by 8. what is the value here 7 by it this value is 7 by 8 so since decreasing so 1 minus 7 by 8 okay since if it is increasing right if something is increasing here you can see if something is increasing for suppose x is being increased by 25 percent it's like x plus 1 by 4 of x it's like x into 1 plus 1 by 4 it's like x into 5 by 4 this 5 by 4 is my multiplying factor 5 by 4 right what is this 1 plus 1 by 4 so you see here what is 1 by 4 so 1 by 4 is our is our 25 value why 1 plus because it is increasing here 7 by 8 is our it is 10.5 percent degrees why 1 minus because it is decreasing here also what is one by five one by five is our twenty percent value why one minus one by five because decreasing so always you can we can generalize it now that to calculate multiplying factor so multiplying factor is always in case of increase it is 1 plus the fraction value in case of decrease it is 1 minus the fraction value okay so 1 plus fraction value and what is multiplying factor multiplying factor okay 1 plus fraction value and 1 minus fraction value always right so for one in one step if i want to write here suppose if i take example um 37 point sorry 27 6 uh 648 if decreased by 37.5 percent what is the result i should directly write i should directly write 648 into 5 by 8 is the answer and solve it right 8 into 81 but the answer answer is 4 05 directly i should do why it now why 8 for fixed 48 into 5 by 8 point because percent thirty seven point five percent it is what it is three by eight degrees for three by eight degrees what is the multiplying factor for decrease one minus fraction value so one minus three by eight that is 5 by 8 should be the multiplying factor right so simply 6 48 into 5 by 8 simply that's it right in one step sorry one step solution okay last slide we did this okay 840 to be decreased by it is 10.5 percent think in mind okay what is what is the fraction value is 7.5 percent seven by so seven by eight degrees so 840 into what into 1 minus 4 degrees 1 minus 7 by 8 that is 1 by 8 that's it what is the answer answer is 1 0 5 cancel it 1 0 5 this 1 by 8 is the multiplying factor right because 7 by 8 degrees means what again what is multiplying factor seven by eight degrees one minus seven by eight is the multiplying factor that is one by eight that is one minus fraction value one by seven by eight right so easy is so so fast it is so easy and so fast okay now see 1212 when decreased by decreased by 83.33 percent i said let's say let's this time increase by increase by 83.33 percent what i should do one two one two into now what is 83.33 percent fraction value five by six so five by six increase five by six increase what is the fraction value of 1 plus 5 by 6 increase so 1 plus fraction now okay so 1 plus 5 which is 6 that is 11 by 6 11 by 6 okay cancelled 2 0 2 times so 2 0 2 into 11 right as it is 202 into 11 it is how much tell me 11 22 is 22 and 11 into 20 is what see 11 you get 2 02 into 11 how you can break it 200 into 11 sorry 200 into 11 is 2200 and 2 into 11 is 22 so it is 20 to 22 that's it is the answer right so why 11 by 6 again same reason because 5 by 6 increase so this 5 by 6 increase is equal to multiplying factor of what 1 plus 5 by 6 that is 11 by 6 this is what ln by 6 so increase 1 plus fraction value decrease 1 minus fraction value okay so we'll continue this initial video thank you [Music]