Question

A number consists of two digits whose sum is 8.If 18 is added to the number its digits are reversed.Find the number.

Answer 1

$let \: the \: ones \: digit \: = x \\ and \: tens \: digit \: = y \\ so \: the \: number \: = 10y + x \\ according \: to \: question \: x + y = 8..........(1) \\ and \: if \: added \: 18 \: the \: number \: => 10y + x + 18 = 10x + y \\ = > 9y - 9x = - 18 \\ => 9x - 9y = 18..........(2) \\ (1) \times 9 => 9x + 9y = 72........(3) \\ (3) - (2) => 18y = 54 \\ so \: y = 3 \\ and \: from \: (1) \: x = 5 \\ hence \: the \: number \: is \: = 10y + x = 10 \times 3 + 5 = 35$

Answer 2

$\huge\sf{\underline{\underline{Solution:}}}$

Given :-

• Sum of 2-digit number = 8

• If 18 is added to the number, the digits change their places.

To Find :-

• The Number

______________________________

Let one of the number be x

And the other number be 8 - x

According to the question

⇒ 10x + (8 - x) + 18 = 10(8 - x) + x

⇒ 10x + 8 - x + 18 = 80 -10x + x

⇒ 9x + 26 = 80 - 9x

⇒ 9x + 9x = 80 - 26

⇒ 18x = 54

⇒ x = 54/18

⇒ x = 3

One Number = x = 3

Other number = 8 - x = 8 - 3 = 5

Hence, the number is 35.