Aptitude - Problems on Numbers - Discussion

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.

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

Can anyone explain it in another way?

Why we take x and 1/8 explain?

What is unit, ten digit and product.

I can't understand. Please explain in a simple way.

Could anyone please provide the shortcut method?

xy = 8
10x + y + 18 = 10y = x
9x - 9y + 18 = 0
x-y = -2
8/y - y = -2
So by solving above equation we get y = 4,
by putting y=4 in xy=8 so we get x = 2.
So the original no. is 10x+y = 24.

Let's not look into the options to solve this. Let's solve from the scratch--
The product of 2 digits is 8:-

1 * 8 = 8
2 * 4 = 8
4 * 2 = 8
8 * 1= 8.

So, the number has to be any of the above-given numbers i.e 18 or 24 or 42 or 81.

Now, add 18 to all the above 4 numbers, only 24 will be reversed after adding 18. => 24 = 42 (reversed).

So, 24 is the answer.

Let the ten's and unit digit be x and 8/x because on multiplying x*8/x we get 8. That's what is actually said at the first line of the question.

Now, suppose let's unit digit be 8/x and ten's digit be x. Now, the number becomes 10 * x + 8/x (let us consider this equation as equation number 1)

According to the question, given that
10 * x + 8/x + 18 = 10 * 8/x + x.

Further Solving by taking L.C.M on both sides we get the statement a 10x^2+8+18x = 80+x^2 (the sign (^) here denotes square of that number).

9x^2 +18x-72=0.

Take 9 as common from above equation, you'll get,
x^2 +2x-8 = 0.
x^2+4x-2x-8 = 0.
x(x+4)-2(x+4) = 0.
(x+4)(x-2) = 0.

Hence
x = 2 (since x = -4 cannot be taken becoz the digit is negative).

Now put x=2 in above equation number 1

Thus 10*x+8/x becomes
=10*2+8/2 (since x=2)
=20+4
=24
Hence the required answer is 24...
Any doubt plz ask ....!!