Question

A number consists of two digits whose sum is 9.if 9 is subtracted from the number , the digits interchange their places.find the number please

Answer 1

let the unit digit be x and the tens digit by y
We are told x+y = 9 **
So the original number is 10y+x

we are told: 10y+x - 9 = 10x + y
9x - 9y = -9
x-y = -1 ***

add ** and ***
2x = 8
x = 4 , then in ** y = 5
so the number is
10y+x
= 10(5) + 4 = 54

check: take 9 from 54 to get 45, which is the original number reversed.

We could have found the answer by using common sense:
we were told the sum of digits was 9
only possible cases :
90 --- take 9 away: 80 <----- not the number reversed
81 --- take 9 away: 72 <----- not the number reversed
72 --- take 9 away: 63 <----- not the number reversed
63 --- take 9 away: 80 <----- not the number reversed
<b>54</b> --- take 9 away: 45 <----- Ahhhh, the number reversed