Question

The sum of the digits of a two digit number is eight the digits are reversed the number increases by 18 find the original number

Answer 1

The two digit number is 35.

Explanation:

Let xy be the two digit number

According to given statement

`x+y = 8\ \ \ \ Eqn\ 1`

The place value of xy is 10x+y

Reversing the number will be: 10y+x

It is also mentioned that the new number is previous number increase by 18

So,

`10y+x = 10x+y+18\\10y-y+x-10x = 18\\9y-9x = 18\\9(y-x) = 18\\(9(y-x))/(9) = (18)/(9)\\y-x = 2\ \ \ Eqn\ 2`

From equation 2

`y = 2+x`

Putting in equation 1

`x+y = 8\\x+2+x = 8\\2x+2 = 8\\2x = 8-2\\2x = 6\\(2x)/(2) = (6)/(2)\\x = 3`

Putting x = 3 in equation 1

`3+y = 8\\y = 8-3 = 5`

xy = 35

Hence,

The two digit number is 35.