Question

what is the original number if the sum of two digit number is 9 and by interchanging the digit new number formed is 9 more than original number ​

Answer 1

Answer:

original number is 45

Step-by-step explanation:

let the number = 10x + y

A.T.Q

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

10y + x = 10x + y + 9

10y + x - 10x - y = 9

9y - 9x = 9

divide by 9

y - x = 1

-x + y = 1 ------(2)

on adding eq 1 and 2

x + y = 9

-x + y = 1

2y = 10

y = 10/2

y = 5

put y in eq 1

x + y = 9

x + 5 = 9

x = 9 - 5

x = 4

original number = 10x + y

= 10 × 4 + 5 = 40 + 5 = 45