Aptitude Day 18

Problems On Ages

1. The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what'll be the ratio of the ages of P and Q after 4 years?

Solution:
         Let the resent ages of P and Q is 6x and 7x respectively.
         If Q is 4 years old than P, then the equation will be 
                7x-6x=4
                     x=4

        The ratio of the ages of P and Q after 4 years will be 6x+4: 7x+4
        By substituting x value, the above equation becomes 28:32
        On further simplification, it becomes 7:8. This will be your answer.

2. At present, the ratio between the ages of P and Q is 4:3. After 6 years, P's age will be 26 years. What's the age of Q at present?  

Solution:
        Let the present ages of both will be 4x and 3x respectively.
       After 6 years, P's age will be 26 years so the equation will be
              4x+6=26 
                   x=5
        The age of Q = 3x=3(5)
                              = 15 years.

3. Present ages of X and Y are in the ratio 5:6 respectively. Seven years hence this ratio will become 6:7 respectively. What's X's present age in years?

Solution:
       Let the present ages of both will be 5x and 6x respectively.
       After 7 years, their ratio will be 6:7 where 6=5x+7 and 7=6x+7. So this becomes
               5x+7/6x+7 = 6/7
               7(5x+7) = 6(6x+7)
                35x+49 = 36x+42
                          x = 7
      X's present is 5x=5(7)
                                = 35 years.