Question

sum of the digit of a two digit number is 9 when we interchange the digits it is found that the resulting new number is greater than the original number by 27 what is two digit number?​

Answer 1

Answer:

Step-by-step explanation:

let the tens place =x

let ones place=9-x

number=10x+1(9-1)

10x+9-x

9x+9

when interchanged

10(9-x)+1x

90-10x+x

90-9x

(90-9x)-(9x+9)=27

90-9x-9x-9=27

81-18x=27

81-18x-81=27-81

-81x=-54

x=-54/-18=3

numbers =10x+9-x

9x+9

9.3+9

27+9

36

Answer 2

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.