Question

if sum of two digits numbers is 9 if we interchange their postion the newno.exceed the original number by 9. find the nnumbersbbv

Answer 1

Explanation:

EXPLANATION.

Let the digit at tens place be = x

Let the digit at unit place be = y

original number = 10x + y

reversing number = 10y + x

To find the number.

=> The sum of two digit number = 9

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

=> If we interchange their position the new

number exceeds the original number by 9

=> 10y + x = 10x + y + 9

=> 9y - 9x = 9

=> y - x = 1 ......(2)

From equation (1) and (2) we get,

=> 2y = 10

=> y = 5

Put the value of y = 5 in equation (1)

we get,

=> x + 5 = 9

=> x = 4

Therefore,

original number = 10x + y = 10(4) + 5 = 45.

Answer 2

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.