Problems on Ages

Most of the problems on ages could be solved by 

• forming linear equations from the relationships or conditions given in the questions
• solving those linear equations to get the required answer.

Here are some solved problems on the ages:

Q1. A got married 8 years ago. A’s 1 present age is 1(1/4) times his age at the time of marriage.A’s son’s age is 1/10 times his present age. His son’s age in years, is
(a) 2        (b) 3
(c) 4       (d) 5

Answer:(c) 4   
Solution:
Let A's present age be x age, then according to the conditions given in the questions, we have
            x = 1(1/4) (x-8)
     =>  x = 1.25(x-8)
     =>  x = 1.25x - 10 
     => 1.25x -x  = 10
            0.25 x   =10
and x = 40 years
Thus, A's son age = (1/10)40 = 4 years

Q2.Three years ago the average age of a family of 5 members was 17 years . A baby having been born , the average age of the family remains the same today. The age of the baby is
(a) 3 years           (b) 2 years
(c) 1 year            (d) 1.5 years

Answer: (b) 2 years
Solution:
Let the age of the baby today is y years.
Then average of the family member today = (20x5+y) /6
But this average is equal to 17.
Thus,    (100 + y) = 17x6
      =>  100 + y = 102
      => y =2 years

Q3. The sum of ages of two brothers , having a difference of 8 years between them, will double after 10 years. What is the ratio of the younger brother to that of the elder brother?
(a) 3:7             (b) 8:9
(c) 10:11         (d) 7:11

Answer: (a) 3:7 
Solution:
Let the age of elder brother be x years and smaller brother be y years. Then given that
                                x - y = 8 ----- (i)
                         and sum is x+y
Again, it is given that the sum of their ages will double after 10 years. The equations thus formed is
        2(x+y) = (x+10) + (y+10)
Thus, 2x + 2y = x+y+20
        => x+y=20 ------ (ii)
adding (i) and (ii), we get
                    2x = 28
                => x = 14 years
and y is 14- 8 = 6 years
Therefore, ratio of younger to elder brother is 6/14 = 3/7