# 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 2 of 5.

Harshit said:   4 years ago
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.

Aaff said:   5 years ago
Thank you for the answer @Anusha.

Sakshi said:   5 years ago
Thanks for the explanation @KCS.

Sarita said:   5 years ago
Thank you for the answer @Anju.

Anju said:   5 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;
(1)

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.

AMIT RANJAN said:   6 years ago
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.

Naina said:   7 years ago
Good Explanation, Thanks @KCS.

Rishitha said:   7 years ago
Can anyone explain what happens after 12k = 48 and 21k = 84?

After we do this how do we get the final answer?