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Linear equations are a very important part of mathematics as a subject. The concept of linear equations is used to solve problems for ages, and in this article, we will look at the different types of problems and how to solve them.
Problems on age are generally about two or more people, and their ages are being compared through using fractions, ratios, and such. One of the skills involved in solving the problems of age is to see what age is of the present and which is of the future.
Various types of questions from problems of ages
Ration and sum of ages
In the problems where the ratio between two ages is given, and the sum of the ages is also provided, we can solve the question by:
Age 1: C Age 2 : D
The ratio between C and D is x:y
The sum of the ages C and D is O
In order to find age C:
C = x / [x+y] X O
In order to find age D
D = y / [x+y] X O
Ratio and product of ages are given
In such cases, we have to compute a relationship between the ratio and the product of the ages and then derive the respective original ages.
The ratio of present and future ages are given
In these old age problems, we have to compute a relationship between present and future ages in order to reach the solution of the problem.
The ratio of past and present ages are given
You will be provided with the ratio between past and present ages. By forming a mathematical relationship between the two, we would need to find the solution. Such problems will be solved after forming a primary equation.
Tips to solve problems on ages
Problems of age and old age problems might confuse or scare you at the beginning, but keeping these few tips in mind can help you solve them with ease. It’s important to stick to the basics and try to solve the question methodically. Here are some tips to solve problems on ages:
The first step should be carefully reading the question and then re-reading it to make sure you are clear. Then you can proceed with forming the main equation that will serve as the backbone of your solution.
It’s important to understand that no complicated calculations are needed in order to reach the solution. Basic mathematical functions such as addition, subtraction, multiplication, and division are enough to find the answer.
The unknown values should be assigned different variables, and the given values should be placed correctly in the equation that you will form.
Forming the equation is the key step to solving problems in ages. Other than that, you simply need to solve the equation through the help of mathematical functions to find the solution to the problem.
Such questions can also be present in complex manners and could be confusing at times. To be methodical is the key approach.
Important formulas to solve problems on age
If the assumed age of the person is Z, then after a time of Y number of years, the age of the individual will be [Z+Y]
If the assumed age of the person is Z, then the individual’s age before Y number of years would be [Z-Y]
If the ages are provided in the form of a ratio in the problems such as R: T, then the age of each individual will be RZ and TZ.
If the assumed age of the person is Z, then Y times the age of the individual would be [ZxY]
If the assumed age of the person is Z, then 1/Y times the age of the individual would be [Z/Y]
Example of a problem on age
Question: the ratio of the age of Rahul and Ram is 6: 8, and the sum of their ages is 56. Then find the age of Ram.
Answer:
We can assume the age of Rahul to be 6x and the age of Ram to be 8x.
Sum of both ages = 6x + 8x = 14x
Now from the question,
14x = 56
X = 4
Then the age of Ram would be = 8 × 4 = 32 years.
Conclusion
Candidates studying for future government examinations should prepare equally effectively for each topic and seek any aid with study materials or preparation ideas. These questions must have some tough effort to complete because age issues are an element of Mathematics. And practice makes perfect, resulting in little or no rough work in the future. You could learn a few techniques and shortcuts from them.
