Question

AA+BB+CC = ABC
Find the values of A,B and C
Note-All numbers are positive and distinct numbers.​

Answer 1

the sum will give maximum,value when A=B=C=9

then, maximum value=99+99+99=297

now AA+ BB CC=ABC

this shows thatABC=297 (if we have to get the maximum value)

Also, this shows that,Value of A can never be greater then 2..coz,max. value is 297..and if A will be greater then 2 then the no. will exceed from the max. value which is not possible..so, possible value of 1 and 2

Now,let's move on the sum...A+B+C=XC (let x on 10th place) this can be possible when C=0and the sum of A+B is 0 or 10

Since we know,that,A+B can only be negative if their value will be same and of negative sign...

but since negative value is not possible so,0 is not possible..the sum off A+B is 10 will be possible if A=1and B=9 or A=2 and B=8other possiblity is not possible because A can have only two value....so,A+B=10. (A=1 and B=9 or A=2 andB=8)also we knowA+B+C+1 =AB put A+B=10then11+C=AB....1)

Now hereAB can be 19 or 28but 28 is not possible because C is single digit and it's value need to be 17,to make sum of 28,which is not possible....so,AB=19......this shows A=1 and B=9nowput it on 1)

We getC=19-11=8so,C=8hence the required no. is 198let's check it11+99+88=198it satisfy the given condition....so solution is exactly right

Answer 2

Answer:

11+99+88=198

Step-by-step explanation:

AA+BB+CC=ABC

Substitute Maximum Posssible Values:

    99+88+77=264

    So,A is less than 300

    (i.e.,) A is 1 or 2 (0 is not Possible because A,B,C are +ve numbers)

=====>Lets take Units digit:

    A+B+C=C

      A+B=0 (0 is a units digit)

      Substitute A values:

         1+B=0        or   2+B=0

         1+9=0(10)    or   2+8=0(10)

         Above solution we get sum as 10 where 1 is a tens digit

                                           and 0 is a units digit.

     We get,

     A=1 and B=9

               (or)

     A=2 and B=8

      11+99+CC=19C   (or)   22+88+CC=28C

        110+CC=19C   (or)     110+CC=28C   28C>264 (Maximum Possible

                                                    sum 99+88+77=264)  

                                                So,it is not Possible.

=======>Lets take Tens digit from 110+CC=19C:

          1+C=9

            C=8

Finally we get A=1 B=9 C=8

   11+99+88=198

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