# Aptitude - Problems on Numbers - Discussion

Discussion Forum : 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 ?
4
8
16
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.

Discussion:
45 comments Page 3 of 5.

Sakshi said:   6 years ago
Thanks for the explanation @KCS.

Sarita said:   6 years ago
Thank you for the answer @Anju.

Chitta meher said:   4 years ago
How come 10 here? Please explain.

Karthik said:   4 years ago
X is in units position and why is in ten's position. So the answer should be 16.

Ajeya said:   6 years ago
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.

Abi said:   6 years ago
Where is the 9 from? Please explain.

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.

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.

Why we have to take 2x in units place rather than x ? can any one explain.

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