Aptitude Day 23

Problem On Ages:

1. The ratio between the present ages of A and B is 5:3. The ratio between the A's age 4 years ago and B's age 4 years hence is 1:1. What's the ratio between the A's age 4 years hence and B's age 4 years ago ?

Solution:
                The present ages of A and B is 5x and 3x respectively.
                A's age (4 years ago) = 5x-4
                B's age (4 years hence) = 3x+4
                Hence,
                        (5x-4)/(3x+4) = 1/1
                          (5x-4) = (3x+4)
                                 2x = 8
                                   x = 4
               The ratio between the A's age 4 years hence and B's age 4 years ago is
                         (5x+4):(3x-4)
                          (20+4):(12-4)
                                 24:8
                                  3:1

2. A is two years older than B who is twice as C. If the total of the ages A, B and C be 27, then how old is B ?

Solution:
                Let C's age be x.
                Then B's age will be 2x and
                          A's age will be 2x+2.
                          Their sum is 27 which is (2x+2)+2x+x = 27
                                                                                5x+2 = 27
                                                                                    5x = 25
                                                                                      x = 5
                 B's age is 2x = 2(5) = 10 years.

3.  A man is 24 years older than his son. In two years, his age will be twice the age of his son. What's the present age of father ?

Solution:
                Let the son's age be x.
                Then the father's age be x+24.
                 After 2 years, his age will be twice of his son,
                            x+24+2 = 2(x+2)
                                x+26 = 2x+4
                                      x = 22
                 The present age of father is x +24 = 22+24 = 46 years.