Question

The sum of the digits of a two-digit number is 12. If the new number formed by reversing
the digits is greater than the original number by 54. find the original number. Check your result ​

Answer 1

Step-by-step explanation:

let the tens digit no. be x and ones digit no. be 12-x .

original no. 10x +12-x = 9x +12

New no = 10(12-x) + x = 120 - 10x +x = 120 - 9x

A/q

120-9x = 9x+12 +54

120-12-54 = 9x+9x

120- 66 = 18x

54=18x

x= 3

Answer 2

Solution!!

Let the numbers of the two-digit number be x and y.

Original number = 10x + y (assumed)

Given that the sum of the 2 digits is 12. So,

x + y = 12...(1)

Given that the new number formed by reversing the digits is greater than the original number by 54. So,

New number = 10y + x

And,

10y + x - (10x + y) = 54

10y + x - 10x - y = 54

9y - 9x = 54

9(y - x) = 9(6)

y - x = 6...(2)

We will add (1) and (2).

x + y + y - x = 12 + 6

2y = 18

y = 9

Putting the value of y in (1).

x + y = 12

x + 9 = 12

x = 12 - 9

x = 3

Original number = 10x + y

Original number = 10(3) + 9

Orginal number = 30 + 9

Original number = 39

Verification!!

x + y = 12

Taking LHS,

3 + 9

= 12

LHS = RHS

Reversed number = 10y + x = 93

10y + x - (10x + y) = 54

Taking LHS,

93 - 39

= 54

LHS = RHS

Hence, verified.