Question

sum of two digits number is 9. when we interchange the digits it is found that the resulting new number is greater than the original no. by 27. what are the two digit numbers?

Explain me.........
Best explanation gets... 40 points + brainliest + three thanks......​

Answer 1

Hey mate ...

here's the answer

Let the digits be x and y.

Then, x+y = 9

the original number is 10x+y.

On reversing, we get the new number as 10y+x

The new number is greater than the old number by 27, i.e.

(10y+x) - (10x+y) = 27

or 9y-9x = 27, or y-x = 3

and x+y = 9

Adding the two equations, we get 2y = 12 or y = 6.

Thus, x = 3.

Therefore, the original number is 36.

Hope it helps ❤

Answer 2

Here's the Solution :

Let the digits of the two digit number be x and y .

So , the number is 10x + y

According to Question

x + y = 9 ------> (1)

And

10x + y +27 = 10y + x

=> 10x - x + 27 = 10y - y

=> 9x + 27 = 9y

=> 9x - 9y = -27

=> 9(x - y ) = -27

=> x - y = -3 ------> (2)

Now adding (1) and (2) we have :

x + y + x- y = 9 -3

=> 2x = 6

=> x = 3

Again : by equation (1)

3 + y = 9

=> y = 9 - 3

=> y = 6

Therefore , required number is

10×3 + 6

= 30 + 6

= 36

Happy Learning