Question

sum of the digita of a two digit number is 11. the given number is less than the number obtained by interchanging the digits by 9. find the number​

Answer 1

Let the number is 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