# Aptitude - Problems on Numbers - Discussion

### Discussion :: Problems on Numbers - General Questions (Q.No.3)

3.

The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?

 [A]. 3 [B]. 4 [C]. 9 [D]. Cannot be determined [E]. None of these

Explanation:

Let the ten's digit be x and unit's digit be y.

Then, (10x + y) - (10y + x) = 36 9(x - y) = 36 x - y = 4.

Video Explanation: https://youtu.be/7QOJjAmGVx0

 Mahantesh said: (Jun 24, 2010) (10x + y) - (10y + x) = 36

 Mahant said: (Jun 24, 2010) Then, (10x + y) - (10y + x) = 36 simlify this

 Venkat said: (Nov 30, 2010) 9x-9y=36 9(x-y)=36 x-y=4.

 Priya P. said: (Dec 2, 2010) Thanks.. Venkat

 Manasa said: (Jul 13, 2011) Explain this step : (10x + y) - (10y + x) = 36 How 10x+y got ?

 Bhupendra said: (Jul 20, 2011) Why would we take 10 we can take 15 or other no also ?

 Shu said: (Jul 21, 2011) Why have they taken 10 only why not 9 or 4?

 Punit Mandelia said: (Aug 1, 2011) Actually it indicates the place, the order of place is hundred tens and unit place. So when we are talking about interchanging digit we are writing in place as we are interchanging there place. Got it.?

 Jisha said: (Aug 3, 2011) Please explain properly step by step.

 Meghna Jain said: (Sep 16, 2011) Please explain in simple form.

 Aravind said: (Jan 14, 2012) Actually here we taken as 2 digit number. i.e, 10*digit1 + digit2 = two-digit number. inter changing.i.e, digit2*10 + digit1 = two-digit number. difference b/w two-digit number & after inter changing that two-digit number is equal to 36. say digit1=x,digit2=y, then, (10x+y)-(10y+x)=36, We get x-y=4.

 Aparna said: (Feb 27, 2012) Thank you Aravind.

 Anshu said: (Apr 5, 2012) Let x and y be two digits of the Numbers. Such that x is in tens position and y is at the ones place So xy is the number xy = 10(x) + y(1) ----------> (1) On interchanging the digits we get yx = y(10) + x(1) ----------> (2) (10x + y) - (10y + x)= 36 10x + y - 10y - x = 36 9x - 9y = 36 x - y = 4

 Swati said: (May 30, 2012) Why in solution its written tens digit be x and unit digit be y? can any one explain me. ?

 Navya Nyeni said: (Jul 25, 2012) Actually we are assuming here as x and y as we need to find d value given you can take any variables to caluculate thats not restricted.

 Prince said: (Aug 25, 2012) Thanks you anshu mam & aravind sir.

 Nikhilesh Israni said: (Jul 30, 2013) Here we are writing the place value of each digit. Suppose we have a number 7245, then the place value of 5 is 5*1=5 and the place value of 4 is 4*10=40. Similarly 2*100=200 and 7*1000=7000. Hence if the number is 'xy' then y's place value is y*1=y and x's is x*10=10x. The same rule applies when we interchange the numbers.

 Nani said: (Aug 2, 2013) Why we are adding 10x+y why n't 10xy?

 Sudha said: (Aug 6, 2013) Why are you taking the 10 digit number. Why not take other digits?

 Shams said: (Sep 11, 2013) Hi, There is not taking 10 digit number. that is the 10th place of number we are finding. see There are 2 two digit is let x and y, So the number will be 10x+y (x is at tenth position & y is at unit position) Because for example number 85. x=8 and y=5. So, 10x+y = ( 10 * 8 + 5 = 85 ). Not do the number (xy = 8*5 = 40) or (10xy = 10*8*5 =400 ). Now for answer proceed further according to question. I think its help to you.

 Bhavya said: (Sep 13, 2013) @Sudha. They take 10 number because of it is in ten's place. So they take 10 number :).

 Sri said: (Jun 4, 2014) Let x and y be two digits of the Numbers. Such that x is in tens position and y is at the ones place. So xy is the number, xy = 10(x) + y(1) ----------> (1). On interchanging the digits we get, yx = y(10) + x(1) ----------> (2). (10x + y) - (10y + x)= 36. 10x + y - 10y - x = 36. 9x - 9y = 36. x - y = 4. This explanation is super @Anshu.

 Sohan said: (Jun 11, 2014) Hello guys, The explanation that all of them have done is extremely excellent. But I have a doubt Can anyone explain me as, if they ask us to find the numbers in same questions. Then what is procedure to be followed. Thank you.

 Pukkaprotagonist@Gmail.Com said: (Jun 20, 2014) Tell me if we have used any formula there or its just common sense :D.

 Mohankumar said: (Aug 20, 2014) To overcome like this problems, you have to know very basic thing i.e how do we expand a number?? eg, 345=3*100+4*10+5*1 right? So now assume digits as xy then u expand it x*10+y*1=xy; Similar way interchange digits xy-->yx isn't it? So expand yx=y*10+x*1; Now you xy-yx=36;(put expanded form in this); Simplify it..

 Sandt said: (Jan 5, 2015) Some time they take 10 digit no x and some time 10x. Why anybody explain me?

 Aparna Devi said: (Jan 21, 2015) Why have they taken 10 only?

 Nishant said: (Feb 2, 2015) Is that method of considering 10 for the units place should be applied for all the problems?

 Arun said: (Apr 3, 2015) I need more explanations for this problem.

 Abdul Kalam said: (May 11, 2015) 9x - 9y = 36. x - y = 4. How did you get 9?

 Suji said: (Jul 14, 2015) Thank you for explanation.

 Vishal Bhosale said: (Jul 15, 2015) Thank you explain it.

 Bhupathi Raj said: (Aug 14, 2015) Anymore shortcut. The answer complete only two steps please explain.

 Abhijit Kale said: (Aug 30, 2015) Guys I agree to this explanation but I found a no which matches the criteria of this question. no is 73. If we reverse is we will get 37. And difference between 73 and 37 is 36. And difference between digits is 3. Am I wrong?

 Abhijit Kale said: (Aug 30, 2015) Guys I agree to your explanation but I found a No. 73. If we reverse it we'll get a no 37. And difference between these two nos is 36. And difference between digits of this no is 3. All these things matches the criteria of this question except my answer. Please rectify me if I am wrong.

 Nagma Jabee said: (Sep 2, 2015) Thanks @Nikhilesh and Isran.

 Qasim said: (Sep 6, 2015) Why do we interchanging the number?

 Balaji said: (Oct 12, 2015) @Abhijit. The number your are interchanging is 73 so you have you have to see the difference between 7 and 3 which is equal to 4. And you can check this with the number 84 & 95.

 Bgnr said: (Aug 4, 2016) Why we take x and why in addition to 10x and 10y, can anyone explain?

 Kama Gupta said: (Aug 24, 2016) By trick, For difference = d/9 and for sum = s/11. So, Difference = 36/9 = 4 (answer).

 Banasree Debbarma said: (Sep 10, 2016) How does 10x, y, 36 come?

 Lakshmi G said: (Oct 31, 2016) Why we take 10 or something digit? They are no mention anything they are mention only 36 find only that one why we take.

 Dennis Joel said: (Nov 23, 2016) Do we have formulae for calculating this? Please tell me.

 Daddi said: (Jan 14, 2017) Yes we have a separate formula for this type of problems. Difference between two digits of two digit number is = (Difference in original and interchanged number)/ 9.

 Vidhya said: (Apr 26, 2017) Instead of 10 can we take anyother number to get the actual answer?

 Bhola Nath Mahakur said: (Nov 25, 2017) Thanks for the explanation.

 Deepak Rawat said: (Dec 5, 2017) We cannot take : (10x+y)-(10y+x)=36 because if x or y = 0 then may it come under one digit number. So, let take : ((10x+10)+y)- ((10y+10)+x)=36 in this way if we put x or y 0. It give result two digit number.

 Tanya said: (Dec 20, 2017) (10x + y) - (10y + x) = 36. Will someone explain to me why we equalize it with 36? Is it because it is stated, "the number obtained by interchanging the positions of its digits is 36". Then please explain me the question " What is the difference between the two digits of that number"?

 Shreya said: (Feb 17, 2018) Thanks for the explantion.

 Mayur said: (Apr 5, 2018) Thanks for the explanation.

 Aakash said: (Aug 22, 2018) Say 1 no is 84. Then interchanging it we will get 48. Difference between these two number is 36. So, the difference between the two digit will be 4.

 Arpish said: (Sep 6, 2018) If in the question it is asked to find the 2 digit number, then how can we find it, can anyone explain?

 Haider Alam said: (Jan 29, 2019) Let the unit place be x. Ten =10x. On interchanging position in difference. 10x-x=39, 9x=36, x=36/9, x = 4 answer. Note : If we don't interchange the value of x will be -4.

 Jeevan said: (Feb 19, 2019) Here, it is given the number obtained by interchanging the position 2 digit number not 1 digit number like 93 - 39 = 36.

 Anoj said: (Oct 16, 2019) How can it solve using only one variable?