Aptitude Day 53

Problems on numbers

1. The sum of the 2 numbers is 15 and their product is 26. What will be the sum of their reciprocals?

Solution:
               Let the 2 numbers be x and y.
               (1/x)+(1/y)= y+x/xy
                                = 15/26.

2.  If the sum of 2 numbers 35 and the sum of their squares is 625. Find their product.

Solution:
                Let the numbers be x and y.
                x+y = 35
                x²+y² = 625

                2xy = x²+y²+2xy-(x²+y²)

                       = (x+y)²- (x²+y²)

                       = 35²-625

                       = 1225-625

                2xy = 600

                 xy  = 300.