Aptitude-Age-Problem - By 10 Times Microsoft Awarded MVP

Problems on Ages

Important Formulae

1. If the current age is x, then n times the age is nx.
2. If the current age is x, then age n years later/hence = x + n.
3. If the current age is x, then age n years ago = x - n.
4. The ages in a ratio a : b will be ax and bx.
5. If the current age is x, then 1/n of the age is x/n

General Tips

1.Use as few variables as possible. One variable is the best.
2.Most age-related problems mention one or more people and one or more points in time (now, in the past, in the future). Write an expression for each possible combination of persons and points in time. For example, if the problem mentions persons A and B and their ages now and 3 years ago then you will write 4 expressions:

A's age now
B's age now
A's age 3 years ago
B's age 3 years ago
4 people and 3 points in time would mean 4*3 = 12 different expressions.

3. As in most word problems it is generally advantageous to make your variable represent the smallest value. This allows you to use addition and/or multiplication to express the other values. In the example above, if A is the younger person, then A's age 3 years ago would be the smallest number. So make "x" represent A's age 3 years ago. And A's age now would be x+3. (B's ages now and 3 years ago would be expressed in terms of x according to the information given in the problem.)
4. Using the relationships described in the problem write as many equations as you have variables. 1 variable -> 1 equation, 2 variables -> 2 equations, etc.
5. Solve the equation (or system of equations)
6. Answer the question! "x" may not be the answer to the question. But you can use "x" and the expressions you wrote in the second step above to answer the question.
Example 1
The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:
Solution

Let the ages of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
3x + 20 = 2x + 40
x = 20.
Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.

Example 2
The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:
Solution

Let the present ages of son and father be x and (60 -x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
54 - x = 5x - 30
6x = 84
x = 14.
Son's age after 6 years = (x+ 6) = 20 years.

Example 3
The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
Solution

Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
Age of the youngest child = x = 4 years.