2023 Mathematics Competition

### Question 29

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### 3 comments

###### Akinola Ajayi

1 year ago

Let the first digit be x

Let the second digital be y

Therefore the number is 10x+y

When reversed the number is 10y+x

(10x+y)-(10y+x) =18>>>>i

x+y=4>>>>ii

From eqn i

10x-x-10y-y=18

9(x-y)=18

Divide both side by 9

x-y=2>>>>iii

Solve eqn ii and iii simultaneously

x+y=4>>>ii

x-y=2>>>iii

Add ii and iii

x+x+y-y=4+2

2x=6

Divide both side by 2

Therefore x=3

Sub x=3 into eqn ii

3+y=4

y=4-3

y=1

Therefore the numbers are 10(3)+1 or 10(1)+3

31 or 13