Aptitude Day 54

Problems on Numbers:

1. Two numbers such that the square of one is 171 less than seven times the square of the other. If the numbers are in the ratio of 2:3, the numbers are:

Solution:

                 Let the numbers be 2x and 3x.

                 7(2x²)-(3x)² = 171

                 28x²-9x² = 171

                 19x² = 171

                     x²=9

                     x=3.

                 The numbers are 6 and 9.

2. The difference of 2 positive integers multiplied by the bigger number is 85 and their sum multiplied by the smaller number is 99. Find the sum of their squares.

Solution:

                Let the bigger number be x and the smaller number be y.

                (x-y)x = 85    [Condition 1]

                 x²-xy = 85   ------- Equation 1

                (x+y)y = 99   [Condition 2]

                 xy+y²=99    ------- Equation 2

                By adding equation 1 and 2, we get

                   x²+y²=184.