# Aptitude - Percentage - Discussion

### Discussion :: Percentage - General Questions (Q.No.4)

4.

What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?

 [A]. 1 [B]. 14 [C]. 20 [D]. 21

Explanation:

Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.

Number of such number =14 Required percentage = 14 x 100 % = 20%. 70

Video Explanation: https://youtu.be/cBamI6iRNIA

 Karthik said: (Jun 9, 2010) Any short cut for this?

 Syed said: (Jun 9, 2010) Ya there is a short cut the concept is : Let's look for the no. whose square ends with 1 from 1-10, we will find that there are only two such number that is 1 and 9. That is between 1-70 there will be 14 such number. Now lets find the percentage. 14 is what percent of 70. 10% of 70 is 7 Therefore 20% of 70 will be 2 * 7 = 14 the answer is 20%.

 Chandrakala said: (Nov 18, 2010) What about 4? 4 is also squre, so 4, 24, 34, 44, 54, 64 also have squre that end in the digit 1.

 Priya P. said: (Dec 2, 2010) @chandrakala Its not end in 1 digit, its end with digit 1 as (1)^2=1 (9)^2=81 ;8(1) got it..

 Saranya said: (Feb 4, 2011) Thank you for your short cut syed.

 Ross said: (Mar 16, 2011) I see that number 10 is not included into consideration even though it has 1 in its digit unit, why?

 Pankaj said: (May 2, 2011) Very good priya.

 Pankaj said: (May 2, 2011) @ ROSS The no 10 after squaring it does not end with 1....... if u square to 1,11,19,21 it ends with 1 Squaring 10 = 10 x 10 = 100 it ends with 0 Squaring 11 = 11 x 11 = 121 it ends with 1 I think u got it.

 Gopal said: (Sep 3, 2011) @pankaj. It is wrong method unit digit means endshould be 1 or 9. And 10 will be end in 0 so 10 is not include.

 Uttam said: (Sep 18, 2011) Inside the 10 there are 2 digits which ends with 1 and 9. Number 70 consists 7 tens. So total no of digits that end with 1 and 9 in 70 are, 7*2=14. So percentage= (14/70) *100=20.

 Joape said: (Oct 31, 2011) It does not count 10, 12, 13, 14, 15, 16, 17, 18. and they did not state about the square in the question.

 Naga said: (Dec 2, 2011) I con't understad this problem

 Daniel said: (May 30, 2012) The question doesn't specify that the digits 1 or 9 must be the last digits, so clearly all the number in the teens, would qualitfy as nubers between 1 and 70 that have the digit 1 OR 9.

 Avnish said: (Jun 24, 2012) In every 10 digits there is 1 or 9 are coming, So we can tell that what is the % of 2 out of 10, That is 20 % only.

 Ravi Teja Adari said: (Aug 5, 2013) Why should take ends with '1'? Why not take other numbers?

 Niraj said: (Dec 10, 2013) What about 12,13,14,15,16,17,18?

 Zaman said: (Dec 17, 2013) We should first understand the question ? The question asks the numbers with 1 or 9 in the unit digit that is in the last digit or ending with 1 or 9. 12, 13, 14 have 2, 3 and 4 in the unit digit respectively.

 Meena said: (Jan 17, 2014) As per the given we should count only the digits which end with either 1 or 9(i.e, units place). Suppose if we consider a no 527. 7 is in units place. 2 in tens place and. 5 is in Hundred's place. In the same we get 1,9,11,19,21,29....so on 14 digits for the above question. To be simple: We have no's end with 1 = 7. We have no's end with 9 = 7. So total = 14. Ans: 14/70*100 = 20%.

 Siddharth said: (Mar 6, 2014) Here's how it is done: From 1 to 10---only 2 numbers have 1 & 9 at unit's place i.e.= 1 &9. Therefore, from 10 to 20---11 and 19 have 1 & 9 at unit's place. Then from 20 to 30---21, 29. From 30 to 40---31, 39 From 60 to 70---61, 69. So what concluded here is that each set has 2 numbers which have 1,9 at unit's place. Therefore: 7 sets=2*7=total 14 numbers.

 Raju said: (Jul 2, 2014) 25% of a number is less than 18% of 650 by 19. Then the number is? Please send me the solution.

 Hanu said: (Aug 1, 2014) They given unit digit is 1 or 9. Suppose take 13 it is 169 so here unit digit is 9 so why it is not correct?

 Kiran Shahzadi said: (Aug 5, 2014) What is mean by unit digit?

 Sameera said: (Aug 7, 2014) Hai raju I can solve your problem: Let us consider the number be = x. 25%of that number = 25*(x/100) = x/4(let us say as y). And also given that 18% of 650 = 18*(650/100) = 117. (Once read 1st line of question). It means that y is less than 117 by 19 so; 117-y = 19. 117-(x/4) = 19. so x = 392.

 Nicky said: (Sep 4, 2014) In question he said 1 or 9 in the units digit there are 4 numbers between 1 to 10 whose unit digit ends between 1 and 9 they are 1, 3, 7, 9 so tell me that what is the solution?

 Harish said: (Oct 15, 2014) @Nicky. I think you know what is unit's digit? So from the given question, we have to count the numbers between 1-70. Which have 1 and 9 in their unit's digit. They are: 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69 these are numbers we are looking for. And these are having only 1 and 9 in their unit's digit. So the count of the above numbers is 14. Then we have calculate the percentage of 14 in 70. So we assume the percentage is x. Hence (x/100)*70 = 14. 70x/100 = 14. 70x = 1400. x = 1400/70 = 20. x = 20%.

 Sreekanth said: (Oct 22, 2014) Why don't you take 12, 13, 14...?

 Phani said: (Nov 30, 2014) Hello friends! in the question, not mentioned that the word "square".

 Ravi Kumar said: (Jan 29, 2015) Hello friends here they asked just between numbers from 1 to 70 so we followed this procedure. It is not easy to find if they asked for larger numbers like 1 to 10000 like this. In this case can't keep go on counting so please tell a new shortcut method.

 Diwaker said: (Jun 30, 2015) What about 12 13 14, 15, 16, 17, 18?

 Aadya said: (Oct 24, 2015) 7x7= 49. 4(9) why don't we count 7 then?

 Emma said: (Nov 12, 2015) Thanks guys I've got the first question so clearly.

 Yashwitha said: (Jun 24, 2016) Then what about the numbers of 11, 12, 113, 14, 15, 19 even 1 is their, then why it is not considered?

 Jeetendra Kushwaha said: (Jun 27, 2016) Please read the question carefully. It says about that number which put in place of a unit and which must be 1 or 9. So only these number are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69. So total 14 numbers.

 Shivaranjitha said: (Jun 27, 2016) Y is less than 117 by 19, means; Either y =117 - 19 or 117 - y = 19. I'm confused with this. Please answer this.

 Tabi said: (Jul 16, 2016) Look again for the definition of "unit's digit". If we have (for the sake of example) --> 180. Then: 1 on '1'80 = hundreds digit. 8 on 1'8'0 = tens digit. 0 on 18'0' = units digit. Therefore, numbers that fulfill the question "What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?" is numbers that have either '1' or '9' on its "units digit". Disclaimer: 10, or 12, 13, 14, 15, 16, 17 and 18 did not make it to the answer because even though they have '1' on its component, that '1'is not a "units digit" since our definition above. The correct numbers are: 1, 9 , 11, 19, 21, 29 , 31, 39, 41, 49, 51, 59, 61, 69. *Counted -> 14 numbers out of 70's. Percentage = (14/70)*100% = 20%. Answer : C

 Honey said: (Jul 22, 2016) Thanks for your clear solution @Tabi.

 Soujanya said: (Jul 22, 2016) What if larger numbers are given? Eg: 1 to 10000. We cannot count manually all the numbers right, Is there any shortcut?

 Gain.... said: (Aug 20, 2016) But they asking 1 or 9 (if they asking instead of this 1 and 9). What will be the answer?

 Amit Das said: (Aug 28, 2016) Why not 12, 13, 14, . , 18? All have 1 in them! It is told 1 OR 9. Not 1 AND 9?

 Ajinkya said: (Sep 9, 2016) 11, 19 is a prime number. So why they are included in squares?

 Uday said: (Sep 13, 2016) We cannot keep 2 digits at a time at a unit place, right. so there should be 1 or 9.

 Smithy said: (Nov 12, 2016) How to find those 14 numbers in between 1-70 is there any shortcut to find it?

 Sarika said: (Dec 10, 2016) Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69. Number of such number = 14. I.E. 100% -------> 70 number. X --------> 14. (100x14) / 70 = 20%.

 Rishav said: (Dec 30, 2016) Why you put 11 21 31and all?

 Arjun said: (Jan 7, 2017) Please explain, what is unit digit?

 Elly said: (Feb 18, 2017) @All. This question has been tricky to understand but thanks to the various explanations. I've got it.

 Kamall Barik said: (Feb 20, 2017) Thanks for your shortcut @Syed.

 Ramesh Kannan said: (Apr 14, 2017) Very easy 100 ÷ 0 = 1.4285714286. Next 1.4285714286 * 14 = 20.

 Panda said: (Apr 26, 2017) Why 1s of 12, 13,14...,18 is not calculated? Please explain.

 Mustafa said: (May 18, 2017) Why 12, 13, 14, 15, 16, 17, 18 are not included?

 Ayas Kanta said: (Jun 7, 2017) Can anyone help me to solve this? A seller got 5% commission on selling for Rs. 10000 and above he got 4% commission. One day he deposited Rs. 31100 in a company after deduction his commission then on that day what was the sale amount?

 Manisha said: (Jun 9, 2017) What percentage of numbers from 1 to 90 has a 1 or 9 as one of the digits? Can anyone solve this?

 Vamshi Sai said: (Jun 18, 2017) I didn't get question properly can anyone help me to get it.

 Cavendish said: (Jun 22, 2017) It has nothing to do with the squares. Just count the numbers ending with 1 or 9 in between 1 and 70 (inclusively). That's all.

 Udit said: (Jun 22, 2017) Why 7 not included? It ends with 9 after squaring.

 Abba said: (Aug 31, 2017) What about 11, 12, 13, 14, 15, 16, 17, and 18?

 Renukanth said: (Oct 1, 2017) What is the need for squaring here, they just asked to find out how man number are there, with the unit digit (1 and 9)?

 Faraz said: (Oct 12, 2017) It is very simple. Now there are 14 numbers which start from 1 or 9 It means 14 out of 70. Now take percentage of 14 out of 70 means multiply by 100 which is equal to 20%.

 Aditys said: (Oct 30, 2017) The question should be 1 and 9 not 1 or 9.

 Daniel said: (Nov 15, 2017) Hey, 10, 11, 12, 13, 14, 15, 16, 17, 18 not count? It have component number 1 too.

 Shaunak said: (Dec 22, 2017) How did we get?

 Subash said: (May 29, 2018) Thank you @Manisha.

 Achyuth said: (Jul 10, 2018) Let's take 100% for all 10numbers placed in the unit digit. Now 2 numbers(1 or 9) it is 20%.

 Laxman said: (Jul 26, 2018) In question there should be 1 & 9 instead of 1 or 9.

 Abhishek said: (Jul 28, 2018) @All. If we increase the parameter from 70 to 100 then what? I mean if we count from 1 to 100 than what will be the solution?

 Abhishek said: (Jul 28, 2018) If we count without unit digit. What is the answer?

 Puja said: (Jul 31, 2018) The Units digit is the digit in the one's column. Ex-4567, 876, 53. Unit digit 7,6, 3. Now come to solution; 1to 70 unit digits are 1,9,11,19,21,29,31,39,41,49,51,59,61,69 =14. So percentage =14/70*100= 20%.

 Annu said: (Sep 24, 2018) The total number is 70. Possible values in number.14. 14 is what % of 70. (14*100)/70. =20.

 Ganesh said: (Nov 20, 2018) Simple 1 or 9 in unit digit in 1st 10 no. Is 2, So 1 to 70 = 2*7 = 14. % = 14/70*100 = 20% Answer.

 Sanjana said: (Jan 6, 2019) Digits with 1 in unitary place:7. Digits with 9 in unitary place:7. 7+7=14, The total numbers=70. 14/70*100=140/7=20%.

 Rekha said: (Feb 13, 2019) 13^2 is 169, so it ends with 9. But why 13 should not be considered b/w them?

 Narendra said: (Mar 1, 2019) I don't understand about value of 14. In question they asking 1 or 9 but not 1&9. They asked about 1 or 9 so how could you consider as 14? Please explain clearly to understand.

 Muskan said: (Mar 28, 2019) I am not understanding, please anyone explain me.

 Preethy said: (May 9, 2019) I am not understanding the answer, please explain it.

 Sanjana said: (May 11, 2019) @Muskan and @Preethy. It is being ask the percentage in two conditions: a) the number should be between 1 to 70. b) the number selected between 1 to 70, it's square should have digit 1 at the end. In simple words, for example the number 11 which consists of digit 1 which satisfies the condition (a) and also it's square (i.e) 121 is also having 1 at end which also satisfies the condition (b) so, this number is taken. Whereas, if we take number 15 which consists of digit 1 in it but it's square (i.e) 225 is not having digit 1 at the end, therefore, it won't be taken. And that how the numbers 1,9,11,19,21,29,31,39,41,49,51,59,61,69 are taken which are 14 in total. Therefore, 14/70 * 100 = 20.

 Shubham Matekar said: (Jul 3, 2019) Why 12, 13... 17 has not considered? Please tell me.

 Sanjana said: (Jul 13, 2019) @Shubham. 12^2 = 144 here, the last digit in 144 is four not "1" that's y 12 is not being taken. Therefore, if the number with the last digit 1 and it's square the last digit is 1 is not being taken! And it's the same with the other number like 13, 17.. and all!! Got it?

 Jim said: (Feb 8, 2020) The question is not talking about ending with 1 or 9, but it's talking about numbers having 1 or 9.

 Basha said: (Jun 30, 2020) In every ten numbers, we have only two numbers that end with digits 1 or 9. So b/w 1 to 70 we 14. (7*2 = 14). Here 7 represents no of tens and 2 represents no of numbers that end with digit 1 or 9. So, 14/70 * 100 = 20.

 Gnanikrishna said: (Aug 4, 2020) What is the unit's digit? Please explain me.

 Durai Arasan T S said: (Aug 14, 2020) Why don't we consider the 12, 13, 18 because it has 1 as a unit digit?

 Arushi said: (Feb 7, 2021) @Jim. The unit digit is the ending digit.

 Villan said: (Feb 22, 2021) The simplest method is by counting the unit places as 3 and 7. So, there are 14 nos. 14/70*100=20 %.

 Aditya Singh Shishodia said: (Mar 2, 2021) @All. Unit place is the first digit and not the last. As per the place value system it would always begin from left to right. This is simply a wrongly phrased question.

 Shivam Tripathi said: (Apr 10, 2021) There are 10 digits from 0 to 9 total( 10 nos) out of which 1 and 9 are asked in question (2 digits) so in question at units place Bo's are not repeating. Hence 2 digits out of 10 digits Make it 20%(2/10=20%). Am I right?