Aptitude Day 19

Problem on ages

1. Ron was 4 times as old as his son 8 years ago. After 8 years, Ron will be twice as old as his son. What're their present ages?

Solution:
           Let son's age 8 years ago be x years. Then Ron's age 8 years ago = 4x.
           Son's present age will be x+8
           Son's age after 8 years will be (x+8)+8 = x+16
           Similarly, Ron's age after 8 years = (4x+8)+8 = 4x+16
           Given: (4x+16)=2(x+16)
                        4x+16=2x+32
                               2x=16
                                 x=8
           The present age of Ron=4x+8=32+8=40 years.
           The present age of son=x+8=16 years.

2. The ratio between the present ages of P and Q is 5:7 respectively. If the difference between Q's present age and P's age after 6 years is 2, what is the total of P's and Q's present ages?

Solution:
           The present age of P is 5x.
           The present age of Q is 7x.
           Given: 7x-5x-6=2 [ Note: We're calculating the ages in present, so we're subtracting 6 from it.]
                             2x=8
                               x=4
           The present age of P is 5x=20 years.
           The present age of Q is 7x=28years.

           Total of P's and Q's present ages = 20+16 = 48 years. 

3. Present ages of Sam and Tom are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What's Tom's present age in years?

Solution:
            The present age of Sam is 5x.
            The present age of Tom is 4x.
            After 3 years, the ratio will be 11:9 and their ages will be 5x+3 and 4x+3 respectively.
            5x+3/4x+3 = 11/9
            9(5x+3) = 11(4x+3)
            45x+27 = 44x+33
                       x = 6

           Tom's present age is 4x = 4(6) = 24 years.