Answer :

Let x and y are the two digits of a two - digit number.

Therefore, the two - digit number = 10x + y and the reversed number = 10y + x

According to the question

⇒ x + y = 9 ……(i)

Also,

⇒ 10x + y – 9 = 10y + x

⇒ 9x – 9y = 9

⇒ x – y = 1 ……(ii)

Adding equation (i) and equation (ii)

⇒ 2x = 10

⇒ x = 5

Hence, y = 9 – x = 9 – 5 = 4

Therefore, the two digit number = 10x + y = (10 × 5) + 4 = 54

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