Question

Sum of the digits of a two-digit number is 12. When we interchange the

digits, it is found that the resulting new number is greater than the original

number by 54. What is the two-digit number?​

Answer 1

Given :-

Sum of the digits of a two-digit number is 12. When we interchange the

digits, it is found that the resulting new number is greater than the original

number by 54

To Find :-

Number

Solution :-

Let the number be ab

a + b = 12 (1)

Now

Interchanged number = 10b + a

10b + a = 10a + b - 54

10b - b = 10a - a - 54

9b = 9a - 54

9b - 9a = -54

9(b - a) = -54

b - a = -54/9

b - a = -6 (2)

Add both

a + b + b - a = 12 + (-6)

2b = 12 - 6

2b = 6

b = 6/2

b = 3

Now

Using 1

a + b = 12

a = 12 - 3

a = 9

Number = 93