Question

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

Answer 1

Hence original number is AB = 39
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Answer 2

Solution

Let the tens place digit be x.

And the unit's place digit be y.

Number = 10x + y

Reversed number = 10y + x

According to the  Question,

1st part,

⇒ x + y = 12

⇒ y = 12 - x .... (i)

2nd part,

⇒ 10y + x = 10x + y + 54

⇒ 10y - y - 10x + x = 54

⇒ 9y - 9x = 54

⇒ 9(12 - x) - 9x = 54    [From Eq (i)]

⇒ 108 - 9x - 9x = 54

⇒ - 18x = 54 - 108

⇒ - 18x = - 54

⇒ x = 54/18

⇒ x = 3

Putting x's value in Eq (i), we get

⇒ y = 12 - x

⇒ y = 12 - 3

⇒ y = 9

Now, Number = 10x + y = 10(3) + 9 = 39

Hence, the required number is 39.