Aptitude Day 65

Problems on Numbers:

1. The sum of the squares of 3 numbers is 122, while the sum of their products taken two at a time is 101. Find their sum.

Solution:

               Let the numbers be a, b and c.

               (a+b+c)² = a²+b²+c²+ 2 (ab+bc+ca)

                               = 122 + 2(101)

                               = 122+202

                               = 324

                  a+b+c  = 18.

               Their sum is 18.

2. The sum of 3 numbers is 90. If the ratio between first and second be 3:5 and the ratio between second and third is 1:2, then the largest number is:

Solution:

               Let the numbers be a, b and c.

               a/b = 3/5 and b/c = 1/2

               Here the b is common in both ratio.

               So,

                    a =3*1 = 3

                    b = 5*1 = 5

                    c = 2*5 = 10

            Now the ratio a:b:c becomes 3:5:10

            If we add the parts, we get 18.

            The largest number is c = (90/ 18)*10 = 50.