Each of 33 cards is printed with a different number. the largest number is 48.when the numbers are added two at a time, the sums are 64, 76 and 84. what is the smallest number?

Dear Student,

Please find below the solution to the asked query:

Given  : Each of 3 cards is printed with a different number and the largest number is 48 .

And

The numbers are added two at a time, the sums are 64, 76 and 84

Let our numbers =  A  , B and C , So

A  + B  = 64                                                 ----- ( 1 ), 

A + C  = 76                                                  ----- ( 2 ) 

And

B  + C  =  84                                               ----- ( 3 )

Now we add equation 1 , 2 and 3 and get

2 A  + 2 B +  2 C =  224

2 ( A  + B  + C ) = 224

A  + B  + C  = 112                                        ----- ( A )

Now we subtract equation 1 from equation A and get

C = 48 

And

We subtract equation 2 from equation A and get

B = 36

And

We subtract equation 3 from equation A and get

A = 28   

Therefore,

Smallest number  =  28                                                                    ( Ans )


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