Question

the sum of the digits of a number is 12 . the given number exceeds the number obtained by interchanging the digits by 36 . find the given number

Answer 1

Step-by-step explanation:

Let the number at tens place be x

Let the number at ones place be y

Original number = 10x + y

New number = 10y + x

Given,

10y + x + 36 = 10x + y

36 = 10x + y - 10y - x

36 = 9x - 9y

Dividing the equation by 9

x - y = 4 (i)

Also Given

x + y = 12 (ii)

Adding equations (i) and (ii)

x + y + x - y = 16

2x = 16

x = 8

Substituting x = 8 in equation (i)

8 - y = 4

8 - 4 = y

4 = y

Given number = 10(8) + 4

= 84