Aptitude Day 22

Problem On Ages: 

1. The ratio between the ages of M and N is 5:6 respectively. If the ratio between the one-third age of M and half of N's age is 5:9, then what's the age of N ?

Solution:
               Let their ages will be 5x and 6x respectively.
               If the ratio between the one-third age of M and half of N's age is 5:9
               Then,
                           1/3(5x) / 1/2(6x) = 5/9
                            9*(1/3)*(5x) = 5*(1/2)*(6x)
                                      3*5x = 5*3x
                                           15x = 15x
               Thus, N's age can't be determined.

2. Ten years ago, A was half of B in age. If their ratio of their present ages is 3:4, what will be the total of their present ages ?

Solution:
               Let the ages(ten years ago) of A and B are x, 2x respectively.
               Their present ages will be (x+10) and (2x+10) respectively.
                 Hence,
                             (x+10)/(2x+10) = 3/4
                               4(x+10) = 3(2x+10)
                                   4x+40 = 6x+30
                                          10 = 2x
                                             x = 5
              The sum of their present ages = (x+10)+(2x+10) = 15+20 = 35 years.