The sum of the digits of a two digit number is 12. if the new number formed by reversing the digits is greater than the original number by 54, find the original number
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In original number, let the tens digit=x and unit place=y and x+y=12
therefore the original number=10x+y
and the reversed number=10y+x
also its given that 10y+x=10x+y+54
i.e. 9y-9x=54
i.e. y-x=6
i.e y=x+6
also y=12-x
i.e. x+6=12-x
i.e. 2x=6
i.e. x=3
also x+y=12
i.e. y=12-x=12-3=9
therefore the original number=39
therefore the original number=10x+y
and the reversed number=10y+x
also its given that 10y+x=10x+y+54
i.e. 9y-9x=54
i.e. y-x=6
i.e y=x+6
also y=12-x
i.e. x+6=12-x
i.e. 2x=6
i.e. x=3
also x+y=12
i.e. y=12-x=12-3=9
therefore the original number=39
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0
Answer:
39
Step-by-step explanation:
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