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. Check your solution.
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let the two digits be x and y
and also let's take x>y
original no = 10x+ y
atq,x+y=12 (1)
reversed no= 10y+x
atq, (10y+x)-(10x+y)=54
=>-x+ y =6 (2) on further reducing
now adding eq (1) and and eq (2) we get
y= 9
substituting y value in eq (1) or (2)
we get x=3
hence original number= (10x + y)=30+9= 39
and also let's take x>y
original no = 10x+ y
atq,x+y=12 (1)
reversed no= 10y+x
atq, (10y+x)-(10x+y)=54
=>-x+ y =6 (2) on further reducing
now adding eq (1) and and eq (2) we get
y= 9
substituting y value in eq (1) or (2)
we get x=3
hence original number= (10x + y)=30+9= 39
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