# 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:
44 comments Page 1 of 5.

Hi I could not understand this problem. Can anyone explain this more clearly please?
(1)

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.

It can't b (x+y) - (x-y).

Rather it could be (10x +y) - (10y + x).

Hi I can't understand this problem. Any more explnation please.

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
(1)

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

Why are we choosing 2x?

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