Question

The sum of the digits of a
two-digit number is 12. If the new number is formed by reversing the digits is grater than the original number by 54,
Find the original number. Check your solution.​

Answer 1

66 is the original number

Answer 2

Answer: 39

Explanation:

Let "x y" be the required two digit number.

The sum of the digits of two digit number = 12

x + y = 12 ------(1)

If the new number formed by reversing the digits is greater than the original number by 54

y x = x y + 54

Let us write this as expanded form

10 y + x = 10 x + y + 54

x - 10 x + 10 y - y = 54

- 9 x + 9 y = 54

Dividing this equation by 9. We will get

- x + y = 6 ------(2)

(1) + (2) x + y = 12

- x + y = 6

___________

2 y = 18

y = 18/2

y = 9

Substituting y = 9 in the first equation.

x + 9 = 12

x = 12 - 9

x = 3

Therefore the required number is 39

Checking:

The sum of the digits of two digit number is 12

3 + 9 = 12

If the new number formed by reversing the digits is greater than the original number by 54

93 = 39 + 54