Question

Sum of the digit of a 2 digit number is 11 . The given number is less than the number obtained by interchanging the digit by 9 .
Find the number

Answer 1

Answer:

Two digit number: xy= 10x+y.

Sum of digits: x+y=11

xy is less then yx by 9: xy+9=yx

xy+9=yx

10x+y=10y+x-9

9x-9y=-9

x-y=-1,

So this is the system of equations to be solved:

x + y=11

x - y =-1

x=5, y=6

The number is 56.

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Answer 2

Answer:

Let the number be XY

Then X+Y=11................... (i)

A.T.Q

10X+Y=(10Y+X)-9

10X+Y=10Y+X-9

10X-X+Y-10Y=-9

9X-9Y=-9

9 (X-Y)=-9

X-Y=-9/9

X-Y=-1 .............................. (ii)

adding both equation, we get..

X+Y=11

- ( X-Y)=-1

_________

2Y=12

Y=12/2

Y=6

Put the value of Y in equation (i)

X+Y=11

X+6=11

X=11-6

X=5

Hence the number is 56

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