the sum of the digits of a two-digit...

Problema Solution

the sum of the digits of a two-digit number is 9. if interchanged, the new number is 9 less than twice the original number. find the numbers.

Let the two digits =x and y

So x+y=9

or x= 9-y

Let the original no = x+10y

After interchanging it becomes = 10x+y

So 10x+y = 2(x+10y) -9

or 10x+y = 2x+20y -9

or 8x-19y= -9

or 8(9-y) -19y =-9

or 72-8y -19y=-9

or 81= 27y

oy y= 81/27=3

So x=9-3=6

So the original no is 6+30=36

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