# The sum of two digits of a number is 12.if 54 is subtracted from it it's digits are reversed.find the number

by Pha

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by Pha

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x+y=12⇒y=12-x.....(i)

ATQ

10x+y-54=10y+x

10x+12-x-54=10(12-x)+x...............(using (i) )

⇒9x-42=120-9x

⇒18x=162

⇒x=9

__LET THE NUMBERS BE X and Y____X+Y=12__

__X=12-Y----------------------1____A.T.Q.____10x+y-54=10y+x____10X-X+Y-10Y=54____⇒9X-9Y=54__

__9(12-Y)-9Y=54__

__108-9Y-9Y=54__

__-18Y=54-108__

__-18Y=-54__

__Y=-54/-18__

__Y=3__

__PUTTING THE VALUE OF Y IN 1____X=12-3__

__X=9__

__HENCE THE NUMBER IS 93__