Question

the sum of the digits of a two digit no. is 11. the given no. is less than the no. obtained by interchanging the digits by 9. find the no.
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Answer 1

Answer:

Step-by-step explanation:

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

Hence the number is XY=56

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