Question

the sum of two digit number is 13 the number formed by interghanging the digit is 45 more than the original number find the original number​

Answer 1

Let unit digit be x and ten's digit be y.

Therefore, original number = 10y + x

Number formed by interchanging digits = 10x + y

ATQ,. x + y = 13 (Sum of digits = 13)

- (1)

10y + x + 45 = 10x + y

10y + x - (10x + y) + 45 = 0

10y + x - 10x - y = -45

9y - 9x = -45

-9x + 9y = -45. - (2)

By elimination method,

Multiplying eq (1) by 9 on both sides

9(x + y) = 9(13)

9x + 9y = 117. - (3)

Adding eq (2) and (3),

-9x + 9y = -45

+. 9x + 9y = 117

______________

18y = 72

y = 72/18 = 4

By ep (1)

x + y = 13

x + 4 = 13

x = 13 - 4

x = 9