Question

the sum of the digits of a two digit number is 10 if 18 is added to the number it's digits are reversed. Find the number ​

Answer 1

The question comprises of two data.

Data 1 :

The sum of digits of a two digit number is 10.

Data 2 :

If 18 is added to the number, it's digits are reversed.

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Let us consider that,

Two digit number = 10x + y

x, y are digits.

From data 1 ; x + y = 10

From data 2 ;

⇒ 10x + y + 18 = 10y + x

⇒ 9x - 9y = - 18

⇒ x - y = - 2

We have two equations now,

x + y = 10

x - y = - 2

⇒2x = 8

⇒ x = 4

Substituting in any equation, We get

⇒x + y = 10

⇒4 + y = 10

⇒y = 10 - 4

⇒y = 6

Therefore, The two digit number is 10(4)+6 = 40 + 6 = 46