# Aptitude - Problems on Numbers - Discussion

### Discussion :: Problems on Numbers - General Questions (Q.No.4)

4.

The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?

 [A]. 4 [B]. 8 [C]. 16 [D]. None of these

Explanation:

Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.

Let ten's and unit's digits be 2x and x respectively.

Then, (10 x 2x + x) - (10x + 2x) = 36

9x = 36

x = 4.

Required difference = (2x + x) - (2x - x) = 2x = 8.

 Ramya said: (Jul 13, 2010) Hi I could not understand this problem. Can anyone explain this more clearly please?

 Pavithra said: (Sep 24, 2010) I get the answer as 16. Diff in digits: (x+y)-(x-y) =2y =2(2x) =4x. Finding the value of x we get, x=4; So ans = 4(4) = 16.

 Sikha said: (Dec 16, 2010) It can't b (x+y) - (x-y). Rather it could be (10x +y) - (10y + x).

 Sravanthi said: (Mar 25, 2011) Hi I can't understand this problem. Any more explnation please.

 Nathi said: (May 4, 2011) At first we should decide the digits of 10's & unit's be X & 2X respectively. ((10 x 2X) + X) - ((10 x X) + 2X) = 36 (20X + X) - (10X + 2X) = 36 21X - 12X = 36 9X = 36 X = 4 The difference between two digits = (2X+X)-(2X-x) = 3X - X = 2X = 2(4) = 8

 Santosh said: (Jun 26, 2011) Why we have to take 2x in units place rather than x ? can any one explain.

 Nagendra said: (Jun 28, 2011) Once u find x then try this method to get the answer 21X-12X 21(4)-12(4) 84-48 that means the two number are 84 and 48.. now we have to take the sum of one no and the difference of other no.. according to question sum of digits and difference of digits that is 48=4+8=12(sum of digits) 84=8-4=4(diff of digits) now the difference of these two answer 12-4=8 Hence the answer is 8.

 Shalini said: (Sep 17, 2011) Why are we choosing 2x?

 Mitali said: (Oct 19, 2011) Here we have The difference between a two-digit number and the number obtained by interchanging the digits is 36 let a,b be 2 numbers so, a-b=36 ratio between the digits of the number is 1 : 2 let x,y be d digits of a number x/y=1/2 so, y=2x now a must be greater than b here we can see y is greater than x here for a => y is ten's digit n x is unit's for b => x is ten's digit n y is unit's so (10y+x)-(10x+y)=36 (10*(2x)+x)-(10x + 2x)=36 (21x)-(12x)=36 9x=36 x=4 (y+x)-(y-x)=(x+2x)-(2x-x)=2x=8

 Virendra said: (Nov 22, 2011) In question diff is given i.e. 36 and ratio is 1:2 We just find out such a pair without calculating.

 Ranjeet said: (Jan 23, 2012) Mitali: Good Explanation from you, thanks.

 Kcs said: (Mar 20, 2012) Two digits x&y x:y=1:2 x=k y=2k two numbers 10x+y&10y+x 10x+y=10k+2k=12k 10y+x=20k+k=21k diff=9k=36 k=4 numbers 12k=48 21k=84 sum of dgts=12 diff of dgts=4 ans=sum-diff=8

 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 Let, x = 2a y = a Then, a = 4 Difference = (8 + 4) - ( 8 - 4) 12 - 4 = 8

 Leopard said: (Apr 18, 2013) Let's the digits are x & y. The ratio between them is x:y = 1:2. So y=2x. Hence y is ten digit no. According to statement, (10y+x)-(10x+y) = 36. (10*2x+x)-(10x+2x) = 36. 21x-12x = 36. 9x = 36. x = 4.. (y+x)-(y-x) = (2x+4)-(2x-4). = (8+4)-(8-4). = 12-4 = 8.

 Deepak said: (Dec 7, 2013) In the first condition, we get, 10x+y-(10y-x) = 36. So, 9x-9y = 36. By solving this we get x-y = 4. Thats all.

 Priya said: (Jul 24, 2014) Can anyone explain why do we take (y+x)-(y-x) in the last step rather than 10x+y-(10y-x) ?

 Pooja said: (Nov 14, 2014) Hello Friends, Suppose x & y two digits and the ratio b/w the digits of the number is 1:2 Therefor, x:y = 1:2 So, y = 2x ..........equation 1. Hence, y is in ten's position and x is in unit place. According to the question, (10y + x) - (10x + y) = 36 From equation 1, we get y = 2x (10*2x + x ) - (10x + 2x) = 36 (20x + x) - (12x) = 36 21x - 12x = 36 9x = 36 x = 4 ........... equation 2. Now putting the value of x in equation 1. y = 2*4 y = 8 Sum and the difference of the digits of the number (x + y) & (x - y) respectively. According to question, Difference between (x + y) & (x - y). = (y+ x) - (y - x) ............. equation 3. Putting the value of x = 4 & y = 8 in the above equation. We get, = (8 + 4) - (8 - 4). = 12 - 4. = 8.

 Manu said: (Dec 7, 2014) Why are you taking (10*2x+x) - (10+2x) = 36? Please explain it.

 Bhavna said: (Dec 17, 2014) Assume the 2 digit number be 84 and by interchanging the digits we get 48. Difference 84-48 = 36. Sum = 4+8= 12. Difference = 8-4 = 4. Difference between sum & diff = 12-4 = 8.

 Chinnadurai said: (Apr 24, 2015) Let digit at 10th place X and unit place Y. From the question: 10X+Y-(10Y+X) = 36. So, 10X-X+Y-10Y = 36. = 9X-9Y = 36. = X-Y = 4. From question Ratio is 1x:2x. Difference between the ratio 1x. So 1x = 4 and 2x = 8. Sum and difference of these two 12, 4 respectively. Then difference between these two 8. Got answer.

 S.prema said: (Jun 12, 2015) Thanks for the explanation.

 Jonsihay said: (Nov 28, 2015) The Problem should be re-stated specially on the aspect of the ratio. It should "NOT JUST BE" 'if the ratio between the digits of the number is 1:2. But it should be restated as 'if the ratio between the unit's and ten's digits of the number is 1:2. Then if that's ok, I think reliably be solvable!

 Rajesh Jangid said: (Jan 18, 2016) Hi can anyone explain when to take 2x and x and when 10x+y-10y-x?

 Aditrya Tiwari said: (Oct 1, 2016) Consider no is 10x + y. Then according to first condition (10x + y) - (10y + x) = 36. On solving this we get, (x - y) = 4. In, the last condition they give, y/x = 1/2. By solving both above equations we get y = 4. They ask the value for,(10x + y) - (10x - y). Which is equal to 2y. Put the value of y. We get final value = 8.

 Rishitha said: (Dec 30, 2016) Can anyone explain what happens after 12k = 48 and 21k = 84? After we do this how do we get the final answer?

 Naina said: (May 4, 2017) Good Explanation, Thanks @KCS.

 AMIT RANJAN said: (Feb 8, 2018) Suppose we take two nos as X & Y, then, 10X+Y-10Y-X=36 => 9X-9y=36 =>X-Y=4 ---> (A) Given, X:Y = 1:2 => X = Y/2 Now from eq (A) , Y/2 - Y = 4 => -Y/2 = 4 => Y= -8 ---> (B) A/Q, (X + Y) - (X - Y) = ? => X + Y - X + Y= ? => 2Y = ? ---> (C) So from (B) putting the value of 'Y' in (C), 2Y = 2 * (-8) = -16 ANS.

 Abi said: (Apr 19, 2018) Where is the 9 from? Please explain.

 Ajeya said: (May 2, 2018) Lets assume n1=10a+b and n2 = a+10b where a and b are digits in a two digit number,given n1-n2 = 36, So, 10a+b-a-10b = 36, 9a-9b = 36, a-b = 4. How can it be 8? Please help.

 Anju said: (Jun 25, 2018) Since they have mentioned the word "difference" in the problem so the answer will be 8 .From the 1st part of the question we can find that X-Y=4, also they have mentioned X/Y=1/2 hence Y=2X; Therefore X~2X=4;hence X=4;Y=8; So, the answer is :(4+8)~(4~8)=8.

 Sarita said: (Sep 26, 2018) Thank you for the answer @Anju.

 Sakshi said: (Oct 23, 2018) Thanks for the explanation @KCS.

 Aaff said: (May 15, 2019) Thank you for the answer @Anusha.

 Harshit said: (Jul 30, 2019) Correct answer should be 16. Ten's digit is X and Unit digit is 2X as the ratio given is 1:2 and not 2:1.

 Vamsikrishnareddy said: (Sep 14, 2019) I am not getting this, please anyone explain me in detail.

 Kolkata said: (Jan 17, 2020) I am not understanding it, please someone explain me.

 Chitta Meher said: (May 26, 2020) How come 10 here? Please explain.

 Karthik said: (Jul 1, 2020) X is in units position and why is in ten's position. So the answer should be 16.

 Md Parvez Islam said: (Sep 24, 2020) Thanks @Chinnadurai.

 Sivasankaran said: (Sep 30, 2020) The given number is 36 which is +ve So the original number should be greater Ex: If ab is two-digit number b is in unit place and a is in 10th place (.etc..hundreds, tens, units) Now the given ratio is 1:2 says that the ratio between 10s or 1s The first number must greater than the reverse digit number. So we give 2x in 10th place in the first number. (Number)(10*2x+x)-(Reverse no-Small)(10x+2x)=36. By solving X=4. Then they said to find the sum and diff of number. Ans=(2x+x)-(2x-x). By solving; We get the Ans is 8.

 Bhargavi said: (Jun 21, 2021) From 3rd question,we can say x-y=4. We have to find diff of ( sum of digits n diff of digits). (X+y)-(x-y)=0. X+y=4. From 2 equations,we get X=4, sub X value then y=0, So 2 numbers are 40 and 04, Sum is 44,diff is 36. So, diff is 44 - 36 = 8.

 Maganizo Chithila said: (Dec 15, 2021) Ratio is 1:2 we will consider 1 and 2 as the numbers. And have variable x after the subtracting. then (21 -12)x=36. Then 9x=36 And x=4 . And have 2x for the second number which is 8. the difference is 8-4 = 4. the sum of 8+4 = 12. Therefore the difference is 12-4 = 8.