Question

The sum of a two digit number and the number obtained by interchanging digits of the number is 154. the digits of the number differ by 2. how many such numbers are there? find all of them.

Answer 1

Let the original number be 10x + y and the number obtained by reversing the digits be 10y + x, then
10x + y + 10y + x = 154
⇒11x + 11y = 154
⇒x + y = 14                      ........(i)

x - y = 2
⇒ x = 2 + y                        .......(ii)

substituting (ii) in (i), we get
2y + 2 = 14
⇒ y = 6
∴ x = 8

Answer 2

Answer:

86 and 68

Step-by-step explanation:

Let the original number be 10x + y and the number obtained by reversing the digits be 10y + x, then

10x + y + 10y + x = 154

⇒11x + 11y = 154

⇒x + y = 14                      ........(i)

x - y = 2

⇒ x = 2 + y                        .......(ii)

substituting (ii) in (i), we get

2y + 2 = 14

⇒ y = 6

∴ x = 8

∴original no=10(8)+6=86

reversing number will be 10(6)+8=68

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