The digit of a two digit number differing 5 if the digit are interchanged and resulting number is at to the original we get 143. what is the number?
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The digit of a two digit number differing 5 if the digit are interchanged and resulting number is at to the original we get 143. what is the number?
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Since this is a two digital number let the digit in the ten's place be [tex]x[/tex] and the digit in the unit's place be [tex]y[/tex].
Thus, the number originally forms [tex]10x+y[/tex].
Now, as per the question:
[tex]y-x=5\\= > x= y-5[/tex]
Upon interchanging, the new number is [tex]10y+x[/tex]
Adding these two numbers, we get
[tex]10x+y+10y+x=143\\= > 11x+11y=143\\= > x+y= 13[/tex]
Use x=y-5 and we get,
[tex](y-5)+y=13\\= > y-5+y=13\\= > 2y=18\\= > y=9[/tex]
So, [tex]x=y-5= 9-5=4[/tex].
The number is,
[tex]4*10 + 9= 49[/tex]