Aptitude - Problems on Numbers - Discussion

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

Mitali: Good Explanation from you, thanks.

Where is the 9 from? Please explain.

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.

Good Explanation, Thanks @KCS.

Can anyone explain what happens after 12k = 48 and 21k = 84?

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

Hi can anyone explain when to take 2x and x and when 10x+y-10y-x?

Thanks for the explanation.

In question diff is given i.e. 36 and ratio is 1:2

We just find out such a pair without calculating.

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.