Aptitude - Problems on Numbers - Discussion

Anyone, please explain this to get it.

Possibilities of getting a product 8 is 24 or 42.
If 18 is added to 42, it gives 60 --> the reversing condition is not met.
Else if you add 18 to 24 --> 18+24 = 42, the reverse of 24.
Hence the answer is 24.

Why X is taken as in the tenth position while 8/X taken as in-unit?

We could have taken X in unit and 8/X in tenth place?

Please explain me.

Two digits let be x and y

So, two digit no. =10x+y.
Given, xy=8.
=>y=8/x or x=8/y...(1).

So, (10x+y) +18=10y+x
=>9x+18=9y
=>x+2=y----(2).

Putting the Value of x from eqn 1 in eqn 2.
8/y-y = -2.
y^2-2y-8 = 0.
y^2-4y+2y-8 = 0.
y(y-4) +2(y-4) = 0.

y = 4/-2, y can't be a negative integer.
So y = 4.
And x = 2.
So, no. is 24.

Well the solution is such that;

Given condition:

xy = 8.
xy*18 = yx.

Now, let tens place be x and ones place be 8/x (using 1st condition).
Using second condition we will have;
10x+8/x+18=80/x+x.
Calculating we get;
x=2 and y=4.

Hence, combining we have and 2,4 i.e,24.

The two digits are 2, 4.
24+18(add 18),
The answer is 42,
Reverse the 42.

Then the final answer is 24.

Lets number is xy;

Given xy=8; -----> (1)
10x + y + 18 = 10y+x.
y-x = 2 ----> (2).

Put y=8/x in (1)
So x^2+2x-8=0;
the root is 2,-4
x=2 so y is 4.

So the number is xy= 24.

I am not understanding this answer.

First let us consider the the number is xy.
Then the number value = 10x+y.

Given that if we add 18 to the number then it would be equal to reverse of the number(yx which value is 10y+x).
i.e 10x+y+18 = 10y+x.
10x+y+18-10y-x = 0.
9x-9y+18 = 0.
x-y+2 = 0 ------------------------------------------------- (1).

But we know product of digits is 8 i.e xy = 8.
then x = 8/y.

so substitute x = 8/y in equation 1.

then 8/y -y + 2 = 0.
i.e 8-y^2+2y = 0.
y^2-2y-8 = 0.

y^2 - 4y-2y -8 = 0.

y(y-4)+2(y-4) = 0.
y= -2 or 4.

we take positive y, then y= 4.
then x= 8/y = 8/4 = 2.

So the number is xy i.e 24.

Answer is absolutely 24. I agree.