Problems based on Age are part of the quantitative aptitude section. Age Equation problems are one of the most important questions that will be asked in all competitive Exams like SSC, IBPS, UPSC, and other State Group Exams. These are algebra-based word problems from which we need to calculate the age of the person or the ratio between the ages by knowing past, present, and future ages of a person or persons. In this article, you will come to know how to solve the age-related problems with Simple tricks and tips.
Age-based problems will be either linear or non-linear, and they will have solutions that will represent the age of the people in question. These Questions are always tricky! So one must read and understand the question to frame equations to solve Age Problems. Equation? Yes, let’s find out the simple equations to be remembered before solving these age-based Questions.
As Age problems are a part of Mathematics, these questions must have some rough work to solve. And practicing makes you perfect, and this results in less or no rough work in the future. You may yourself find out some tricks and shortcuts from them.
Process of Solving Age Problems- Step by Step
- First of all, understand the question carefully. If you understand the information in the question, the solution immediately flashes into your mind.
- Try to split the given information in the question. Because when we split the given information into two or more parts, we can understand them easily.
- Once we understand the given information clearly, solving the “problems on age” would not be a challenging work.
Some basic ideas in Problems on Ages
You need to know that the age or the person is incremented by one by every year and difference of the ages of two persons in constant at any time. Let’s discuss one basic concept behind this Topic. First of all, you must gather following information from the asked question.
- How many persons are mentioned in the question?
- What is their Past age?
- What is their Future Age?
- What is their Present Age?
Here is the concept-
If x = present age of a person
x – 5 = age of the person 5 years ago
x + 5 = age of the person after 5 years
If
A = present age of Ram and
B = present age of Shyam
Sum of their ages 4 years ago = (A – 4) + (B – 4)
Sum of their ages after 2 years = (A + 2) + (B + 2)
Difference of their ages = A – B
Notes:
The age k times would be kA
If ages are given in form of ratio P: Q then, then P: Q would be PA and QB respectively.
Problems based on present age
Case 1: Whole number form
Numerical: The age of mother is thrice that of her daughter. After 12 years, the age of the mother will be twice that of her daughter. What is the present age of the daughter and mother?
Solution: Let the age of daughter be x and that of mother will be y. And the first line clearly states that at present the age of mother is thrice of daughter. Therefore, y = 3x. Now, after 12 years i.e. x + 12, mother’s age after twelve years would be (y + 12) and also it will be twice of her daughter, y + 12 = 2(x + 12).
The final equations are:
y = 3x
y – 2x = 12
Substituting first equation into second and solving we get,
x = 12 years and y = 36
Case 2: Fractional Form
Numerical: Veena’s age is 1/6th of her father age. Veena’s father age will be twice of Arjun age after 10 years. If Arjun’s 8th birthday was celebrated 2 years ago. Then what is the present age of Veena?
Solution: If you read the question. You’ll find three people here and you must be worried how to solve equations of 3 variables. But do not panic. Just make the equations. First, let age of Veena be x and of his father be y. And it’s Cleary stated that the age of Veena is 1/6th of his father. Therefore, x = 1/6y. Now assume Arjun’s age be z, so after 10 years Arjun age would be z+10 and Veena’s father age will be twice of Arjun. Hence, y+10 = 2(z+10). Also, Arjun was of 8 years old 2 years ago. Thus, present age of Arjun = 8 + 2 = 10 = z.
The final equations are
x = 1/6y
y + 10 = 2 (z+ 10)
z = 10
Substituting z = 10 in 2 equation we can easily get the age of Veena’s father to be 30 and then we can calculate present age of Veena.
x = 5
Case 3: Combination of Ratio and Fraction form
The ratio between Satyaa and Bheemaa is 5:6 respectively. If the ratio between 1/3rd age of Satyaa and half of Bheemaa’s age is 5: 9. Then what will be Bheemaa’s present age?
Since, the ratio between Satyaa and Bheemaa is 5:6. Therefore, their present age would be 5x and 6x respectively. Also, the ratio between 1/3rd age of Satyaa i.e. 1/3 * 5x and half age of Bheemaa i.e. ½ * 6x is 5:9.
Therefore, the final equation using the given info would be
5x/3/3x = 5/9
Solving the above equation, we get,
1 = 1
Thus, the present ages cannot be determined with the given information.
Problems based on age before k years
Case 1: Fractional Form
Numerical: Seetha got married 8 years ago. Today her age is 1 2/7th times her age at the time of her marriage. At present her daughter’s age is 1/6th of her age. What was her daughter’s age 3 years ago?
Solution: Let present age of Seetha be x. At present, his age is 9/7th of the age when she got married and it’s been 8 years since she got married. Therefore, her age would be x – 8 when she got married and her present age is 9/7(x – 8). Also, currently her daughter’s age is 1/6th of her. Let the present age of her daughter be y.
The final equations are
x = 9/7* (x – 8)
y = x/6
Solving the first equation, we get age of Seetha = 36 years.
Hence her daughter’s present age is 6 years but we need her age 3 years back. So, she would have been 3 years old.
Case 2: Ratio Form
Numerical: The present age of Arun and his father are in the ratio 2:5. Four year hence the ratio of their ages becomes 5:11 respectively. What is the father’s age five years ago?
Solution: It’s given in question that the current age of Arun and his father are in ratio 2:5. Their present age would be 2x and 5x resp. Four years from now i.e. 2x + 4 and 5x + 4 the ratio between their ages become 5:11
The final equation is
(2x + 4)/ 5 = (5x + 4) / 11
22x + 44 = 25x + 20
X = 8
Age of Arun and his father is 16 and 40 resp.
Therefore, five years ago Arun’s father age = 40 – 5 = 35 years.
Problems based on age after k years
Case 1: Whole number form
Numerical: The sum of present ages of father and son is 8 years more than the present age of the mother. The mother is 22 years older than the son. What will be the age of father after 4 years?
Solution: Again, there are 3 people in this question. Thus, three variables. Let present age of father, son and mother be x, y and z resp. Since, the sum of the present ages of father and son is 8 years more than the mother i.e. x + y = 8 + z.
Also, mother is 22 years older than son, z = 22 + x. We need to find age of father after 4 years i.e. y + 4
The final equations are
x + y = 8 + z
z = 22 + x
Substituting the value of second equation in first we get,
x + y = 8 + 22 + x
y = 30
Therefore, y + 4 = 34 years.
Case 2: Ratio Form
Numerical: The ages of A and B are in the ratio 6:5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years?
Solution: This one is a very simple question. The ratio between ages of A and B is 6:5. Thus, their present age is 5x and 6x resp. And also, the sum of their ages is 44 i.e. 5x + 6x = 44
Solving the equation,
6x + 5x = 44
X = 4
But, we need to find the ratio of their ages 8 years from now.
Thus, their present ages are 24 and 20 respectively.
After 8 years, their ages will be 32 and 28 and hence, the ratio would be 32:28 i.e. 8:7
Case 3: Combination of age after k years and before k years.
Numerical: The ratio between the present ages of A and B is 5:3. The ratio between A’s age 4 years ago and B’s age 4 years hence is 1:1. What is the between A’s age 4 years hence and B’s age 4 years ago?
Solution: You may find this question a bit confusing coz of its language. No worries, it’s not that difficult. Just read the question and form equations using the information given like this. It’s been given the ratio between the present age of A and B is 5:3. Thus, their present age would be 5x and 3x respectively. Now, 4 years ago the ratio between A’s age and B’s age 4 years hence is 1:1. The age of A 4 years ago would be 5x – 4 and age of B 4 years from now will be 3x + 4. And the ratio of this is 1:1 i.e. (5x – 4)/ (3x + 4) = 1/1. But we need to calculate the ratio between A and B such that (5x + 4) :(3x – 4)
The equation is as follows,
(5x – 4)/ (3x + 4) = 1/1
Solving it we get,
x = 4
Hence, A’s current age is 20 and B’s present age is 12
Now putting this value in (5x + 4) :(3x – 4)
We get, 24:8 = 3:1
Practice Questions on Problems on Ages for Competitive Exams
Now you would have got the concept and Tricks behind solving these age-based problems for all Competitive Exams. We will Start with some Questions to make you perfect in this Chapter. Here, Schools360 is providing Free Download links for around 2000+ Questions and Books for you to practice at home.
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Conclusion
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