# 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
Answer: Option
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 2 of 5.

Jonsihay said:   8 years ago
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!
(1)

Leopard said:   1 decade ago
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.

Maganizo Chithila said:   2 years ago
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.
(9)

Anju said:   6 years ago
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.
(1)

Bhargavi said:   3 years ago
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.
(6)

Kcs said:   1 decade ago
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

Bhavna said:   9 years ago
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.

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.

How can it be 8? Please help.

Swamy said:   7 months ago
Let's assume 2 digit number is 10.

10x - 01x = 36,
9x = 36,
x = 4.
Coming to question; 1:2;
1x:2x.
1x4: 2x4.
4:8.
Then the answer is 8.
(12)

Pavithra said:   1 decade ago
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.

Post your comments here:

Your comments will be displayed after verification.