# 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 ?

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 2*x* and *x* respectively.

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

9*x* = 36

*x* = 4.

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

Discussion:

45 comments Page 2 of 5.
Vamsikrishnareddy said:
5 years ago

I am not getting this, please anyone explain me in detail.

Harshit said:
5 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:
6 years ago

Thanks for the explanation @KCS.

Sarita said:
6 years ago

Thank you for the answer @Anju.

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.

Therefore X~2X=4;hence X=4;Y=8;

So, the answer is :(4+8)~(4~8)=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.

How can it be 8? Please help.

So, 10a+b-a-10b = 36,

9a-9b = 36,

a-b = 4.

How can it be 8? Please help.

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.

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.

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