Proportion Based Age Problems

In Proportion Based Age Problems, the problems on the age of a number of individuals will be present in the form of a proportion. Using these proportions you will have to make or formulate an equation or a couple of these. These equations will let you know what the age of these individuals is. Here we will see many such examples of these questions. We will see several examples of these solved examples and formulate methods to solve this section with higher accuracy and in lesser time.

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Proportion Based Age Problems

Let us first see what a proportion is. Suppose the age of your father is 60 years. And let us suppose that the age of your brother is one third the age of your father. What is the age of your brother then? The answer is simple. First, you need to see what the proportion here is. The age of your brother is proportionate to the age of your father. Therefore we can say that the age of your brother is = 1/3[60] = 20 years.

Example 1: There are two people A and B. The difference between their ages is 16 years. If 6 year ago, the elder one was 3 times as old the younger one, find their present ages:

A)

Answer: Let the age of the younger person be = x years. Therefore the age of the older person will be x + 16 years. Notice that we have not used a different variable for the second person. Now let us move on to the second part of the question.

Six years ago the younger one would be x – 6 years old and the elder one would be (x + 16 – 6) years old. As per the question we have:

x + 16 – 6 = 3[x – 6] or x + 10 = 3x – 18.

Therefore we can write, 2x = 28 or x = 14 years old. Thus the age of the elder person will be 14 + 16 = 30 years.

Now let us practice this a bit. If your brother’s age is also proportional to your age, can we find your age? Let us say that your brother is half the age that you are. Then what is your age? Your age is twice the age of your brother which makes you forty years old. Now that we have an idea about how proportions work, let us see some solved examples from this section.

Learn Ratio Based Age Problems here. 

Solved Examples

Example 2: Khan’s age fifteen years from now will be five times his age 5 years ago. What is the present age of Khan?
A) 10 years               B) 14 years                      C) 13 years                    D) 8 years

Answer: Let the present age of Khan be equal to x years. Then Khan’s age fifteen years from now is x + 15 years. Five years ago Khan’s age would have been equal to x – 5 years. Now that we have represented all the conditions let us formulate the equations.

From the question, we have (x + 15) = 5×(x – 5). In other words, we can write 5x – x = 15 + 25. Thus we have, 4x = 40 or x = 10 years. Therefore the present age of Khan is 10 years and the correct option here is A) 10 years.

We can solve the above question in another way too. We could have said that the age of Khan fifteen years from now be x. That will mean that the present age of Khan will be x – 15 years. This is essentially the same equation but will be a bit lengthier. To get a consistency with your methods, you should always select the present age as = x years and work your way up from there.

Example 3: Khan’s father says to Khan, “Son! I was as old as you are at the present at the time of your birth”. If Khan’s father’s age is 38 years now, then the son’s age five years back was:

A) 19 years                  B) 14 years                    C) 13 years                          D) 38 years

Answer: Let the present age of Khan’s father be equal to x years. The present age of Khan’s father is 38 years. So at the time of the birth of Khan, his father would be (38 – x) years old. As per the question, we have:

x = (38 – x) or in other words we can write, 2x = 38 or x = 19 years. So the present age of Khan is 19 years and thus his age five years ago would have been 19 – 5 years = 14 years. Thus the correct option is B) 14 years.

Learn Equation Problems of Age here.

Practice Questions

Q 1: A person A is two years older than another person B. The person B is twice as old as a third person C. The sum of the total ages of the three people is 27 years, then how old is B?

A) 10 years                  B) 11 years                 C) 12 years                   D) 13 years

Ans: A) 10 years.

Q 2: The present age of a person is two-fifths of the age of his mother. Eight years hence, his age will be half the age of his mother. What is the present age of the mother?

A) 30 years               B) 40 years               C) 50 years                      D) 60 years

Ans: B) 40 years

Q 3: Ten years ago, some person P was half the age of another person Q. If the ratio of the present ages of the two people is 3:4, then the sum of the ages will be:

A) 25 years                  B) 30 years                 C) 35 years                    D) 40 years

Ans: C) 35 years