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