Aptitude Day 55

Problems On Numbers

1. The difference between the squares of two numbers is 28000 and the sum of their numbers is 400. Find the numbers.

Solution:
                Let the 2 numbers be x and y.
                (x²-y²) / (x+y) = 28000/400

                (x+y)(x-y) / (x+y) =  70

                x-y = 70 ------ Equation 1

                x+y = 400 ---- Equation 2

                By solving equations 1 and 2 we get,

                x = 235 and y = 165.

                The numbers are 235 and 165.

2. The sum of three consecutive numbers is 315. The middle number is:

Solution:

                Let the numbers be x, x+1 and x+2.

                x+x+1+x+2 = 315

                3x+3 = 315

                    3x =  312

                      x = 104.

                The middle number is x+1 = 105.