Question

If N is two digit no. whien digits are interchanged,we get another prime no. M. if N + M =176 then find N-M.

Answer 1

now N + M = 176. SO N = 1OX + Y AND INTERCHANGING NO = 10Y + X . NOW ADD IT. 1OX+Y+1OY+X=176. AND THEN 11X+11Y=176 AND THEN X+Y=16 SO NOW SUBTRACT IT WITH N= 1OX+ Y WE GET N-16=9X.... TAKE IT AS EQATION 1,AND AGAIN SUBTRACT X+Y = 16 WITH M= 1O Y+ X WE GET M-16= 9 Y....... TAKE IT AS EQATION 2, NOW FROM QUETIONANSWER 1 AND 2 WE GET OUR ANSWER . THANKS

Answer 2

Answer :

Let N  =  10x  +  y  

And , when digits are interchanged,we get another prime number M . So

M  =  10y  + x  

Given

N  +  M  =  176  , So

10x  +  y +  10y +  x =  176  

11x +  11y =  176

11 (  x  +  y  )   =  176

x  +  y  =  16

So,

Possible values of x and y  7  ,  9  and  8   ,  8

But If we have x  and y  8   ,  8  

Then we get M  =   88  , That is not a prime number , So we take

x and y  =  7 ,  9

So,

If

N  =  79  , Then M  =  97  

So,

N  -  M  =   79  - 97    =   - 18

And

If

N  =  97  , Then M  = 79

So,

N  -  M  =   97  - 79   =   18