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Aptitude Day 35


Problems on Numbers

1. The sum of the 2 numbers is 13 and the sum of their squares is 85. Find the numbers. 

Solution:
                  Let the numbers be x and (13-x).
                            x2+(13-x)2=85    [Given condition] 
                            x2+169-26x+x2=85
                            2x2-26x+84=0
                             x2-13x+42=0
                             x2-7x-6x+42=0
                             x(x-7)-6(x-7)=0
                              (x-7)(x-6)=0
                                  x=7, 6.
                  The two numbers are 7 and 6.           

2. If the sum of the two numbers is 22 and their product is 40. Find the difference between the 2 numbers.

Solution:
                 Let the numbers be x and y.
                  x+y = 22 and xy = 40 [Given]
                  (x-y)2= (x+y)2 – 4xy    [Since (x+y)2 – 4xy = x2+2xy+y2-4xy  = x2-2xy+y2]  
                           = (22)2-4(40)
                           =484-160
                  (x-y)2= 324
                     x-y = 18
         

                    


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