# HOW TO SOLVE PROBLEMS ON AGES

## About the topic "How to Solve Problems on Ages"

How to solve problems on ages ?

This is a big question having had by the people who are preparing for competitive exams. In this section, we are going to learn, how to solve problems on ages step by step.

## Steps Involved in Solving Problems on Ages

To get answer for the question "How to solve problems on ages ?", we have to be knowing the following steps explained.

Step 1 :

Understanding the question is more important than any other thing. That is, always it is very important to understand the information given in the question rather than solving.

Step 2 :

If it is possible, we have to split the given information. Because, when we split the given information in to parts, we can understand them easily.

Step 3 :

Once we understand the given information clearly, solving the  problems on age would not be a challenging work.

Step 4 :

When we try to solve the problems on ages, we have to introduce "x" or "y" or some other alphabet for unknown value (=answer for our question). Finally we have to get value for the alphabet which was introduced for the unknown value.

Step 5 :

If it is required, we have to draw picture for the given information. Drawing picture for the given information will give us a clear understanding about the question. For most of the problems on ages, picture will not be required.

Step 6 :

Using the alphabet introduced for unknown value, we have to translate the English statement (information) given in the question as mathematical equation.

In translation, we have to translate  the following English words as the corresponding mathematical symbols.

of -------> x (multiplication)

am, is, are, was, were, will be, would be --------> = (equal)

Step 7 :

Once we have translated the English Statement (information) given in the question as mathematical equation correctly, 90% of the work will be over. The remaining 10% is just getting the answer. That is solving for the unknown.

These are the steps most commonly involved in "How to solve  problems on ages".

We hope, the steps explained above will give a clear answer for the people who have the question " How to solve problems on ages ?"

Let us look at, how these steps are involved in solving problem on ages given below.

Problem :

The age of a man is three times  the sum of the ages of his two sons and 5 years hence his age will be double the sum of their ages. Find the present age of the man.

Solution:

Step 1 :

Let us understand the given information. There are two information given in the question.

1. The age of a man is three times the sum of the ages of his two sons. (At present)

2. After 5 years, his age would be double the sum of their ages. (After 5 years)

Step 2 :

Target of the question :

Present age of the man = ?

Step 3 :

Introduce required variables for the information given in the question.

Let "x" be the present age of the man.

Let "y" be the sum of present ages of two sons.

Clearly, the value of "x" to be found. Because that is the target of the question.

Step 4 :

Translate the given information as mathematical equation using "x" and "y".

First information :

The age of a man is three times the sum of the ages of his two sons.

Translation :

The Age of a man ----->  x

Is ----->  =

Three times sum of the ages of his two sons ----->  3y

Equation related to the first information using "x" and "y" is

x  =  3y ------(1)

Second Information:

After 5 years, his age would be double the sum of their ages.

Translation:

Age of the man after 5 years -----> x + 5

Sum of the ages of his two sons after 5 years is

-----> y + 5 + 5  =  y + 10

(Here we have added 5 two times.The reason is there are two sons)

Double the sum of ages of two sons -----> 2(y + 10)

Would be ----->  =

Equations related to the second information using "x" and "y" is

x + 5  =  2(y + 10) -----(2)

Step 5 :

Solve equations (1) & (2) :

Plug x  =  3y in equation.

(2) ----->  3y + 5  =  2(y + 10)

3y + 5  =  2y + 20

y  =  15

Plug y = 15 in equation.

(1)-----> x  =  3 ⋅ 15

x  =  45

Hence, the present age of the man is 45 years.

After having gone through the stuff given above, we hope that the students would have understood "How to Solve Problems on Ages"

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