Aptitude - Problems on Numbers - Discussion

@Vinod. How x-y=-2 suddenly comes, next step what formula is that?

Two digit number 10x+y.

xy = 8.

10x+y+18 = 10y+x.

x-y = -2.

(x+y)^2 = (x-y)^2+4xy.

= (-2)^2+4*8 = 36.

x+y = 6.
x-y = (-2).

x = 2.
y = 4.

Answer 24.

9x2+18x-72.

How it is simplified further?

Can you said in another way?

Only 24 is the product of 8 in this number. So answer is 24.

How can solve like this manner 8+18 = 24?

8+18 = 26. It's wrong. The product of the number is 8 not that number.

First we have to check with the options then only we find answer easily.

Here the first condition is that the multiple of that two digit number is 8.
Then we check all the options. Given four options satisfying the 1st condition.

Now go to 2nd condition, i.e if 18 is added to that two digit number the answer will be reversed.
So we can check through all the options then we get 24 is the correct option.

i.e 2*4 = 8.
24 + 18 = 42.

Hence the 2 conditions are satisfied.

Above you write 8+18 = 24 but 8+18 is 26 how it is to be 24?

Two digits=x & y so two digit no = 10x+y.
Product of digits is x*y = 8.

So (10x+y)+18 = 10y+x.
i.e x-y = -2......(1).
as x*y=8 so x = 8/y.

Hence equation (1) becomes 8/y-y = -2......(2).
Solving equation(2) we get y = 2.

Putting y=2 in equation (1) we get x = 4.
So the two digited number xy = 42.

So please tell me how answer comes to 24.
Please correct me if I am wrong?

Why 18 should be added in the option to get the answer?