Aptitude - Problems on Numbers - Discussion

In the first condition, we get,
10x+y-(10y-x) = 36.

So, 9x-9y = 36.
By solving this we get x-y = 4. Thats all.

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.

Let x and y be two digits of the Numbers.
Such that x is in tens position and y is at the ones place
So xy is the number
xy = 10(x) + y(1) ----------> (1)
On interchanging the digits we get
yx = y(10) + x(1) ----------> (2)
(10x + y) - (10y + x)= 36
10x + y - 10y - x = 36
9x - 9y = 36
x - y = 4
Let,
x = 2a
y = a
Then,
a = 4
Difference =
(8 + 4) - ( 8 - 4)
12 - 4 = 8

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

Mitali: Good Explanation from you, thanks.

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

We just find out such a pair without calculating.

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

Why are we choosing 2x?

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

Hence the answer is 8.

Why we have to take 2x in units place rather than x ? can any one explain.