Problems on ages is a crucial component of the quantitative aptitude section. Solving age related problems requires logical reasoning, algebraic equations, and a clear understanding of the given information. As easy as they might sound problems on ages can tend to be tricky and time-consuming, leading to confusion and mistakes. With problems based on ages it is important we master the fundamental concepts, and practicing extensively.
This blog post is a comprehensive guide to help you master age-related problems in the context of quantitative aptitude. We will explore the different types of age problems encountered in exams, the essential strategies for solving them, advanced techniques and shortcuts. By the end of this guide, you will be able to tackle age-related problems with confidence and accuracy, and improve your overall performance in quantitative aptitude exams.
Understanding Problems on Ages
When solving age problems we look for information such as
- Present age of one or more individuals
- The relationships between the individuals or their age difference.
- Additional conditions if any.
For unknown ages, we basically assign variables and form equations. Using algebraic techniques is the crux of solving problems on ages. We capture the relationships between individuals, age differences or conditions using equations.
Tips to Solve Problems on Ages
Age problems are based on ages of the people in present, past or the future.
When solving these problems,
- Formulate equations:
Based on the given information, Respresent unknown ages using variables.
- If the current age is x, then the age after n years will be (x+n) years.
- If the current age is x, then the age before n years will be (x-n) years.
- If the age of two individuals is in the form of ratio m:n, we consider their age to be mx and nx respectively.
- Using the variables and based on the relationship defined in the problem form an equation.
For instance, consider this example.
Example : In 6 years Krishna will be twice the age he was 4 years ago. What is his present age?
The problem talks about Krishna’s present age, his age 6 years hence and 4 years ago. So, by considering Krishna’s present age to be x, his age after 6 years will x+6 and 4 years before will be x-4.
Given that, Krishna’s age in 6 years will be twice the age he was 4 years ago=>
x+6 = 2 (x-4)
x = 14
Hence Krishna’s present age is 14 years.
- Map the Age differences:
If the relationships between the individuals is expressed as differences, try to map the difference into equations and solve for the unknowns:
Example: The sum of the ages of a father and his son is 50 years. The father is four times as old as the son. Determine their ages.
Let’s assume the son’s age as ‘x’ years. The father’s age would be ‘4x’ years.
Based on the given information, we can create the equation: x + 4x = 50
Simplifying the equation, we find: 5x = 50 x = 10
Therefore, the son’s age is 10 years, and the father’s age is 4×10 = 40 years.
- Check for Past or Future Ages:
Few of the age problems involve past or future ages depending or conditions or time intervals. These changes in age must also be used while creating the equations.
Example: Five years ago, Jane was three times as old as Sam. Determine their current ages if the sum of their ages is 40 years.
Let’s assume Sam’s current age as ‘x’ years. Jane’s current age would be ‘y’ years.
Based on the given information, we can establish the equation: y – 5 = 3(x – 5)
Since the sum of their ages is 40 years, we have the equation: y + x = 40
Simplifying the equations, we find the values of x and y: y – 5 = 3x – 15 (from the first equation) y + x = 40 (from the second equation)
Solving the equations, we find: x = 15 y = 25
Therefore, Sam’s current age is 15 years, and Jane’s current age is 25 years.
Problems on Ages – Quiz
Problems on Age - Exercise - Blog
14 questions
- Ajith is 15 years younger than Ravi. 5 years ago Ravi was twice Ajith's age. What is Ajith's present age?
- 20
- 12
- 23
- 21
Show the answer
Answer: 20
The problem talks about two people Ajith and Ravi, and their current age and their age 5 years ago. Let Ajith's present age be $x$, then based on the information given, If Ajith is x years old, then Ravi is $x$+15 years old. 5 years ago Ajith was $x$-5 years old and Ravi $x$+10 years old Given that, 5 years ago Ravi was twice Ajith's age : 2x($x$-5).
$x$ + 10 = 2($x$-5)
$x$ = 20.
Hence Ajith's current age = 20.
- Anil's age is twice that of Chaitanya, who is three years younger than Advith. The sum of their ages is 63. Find the age of each Advith?
- 15
- 24
- 18
- 21
Show the answer
Answer: 18
In the problem, we are given with the details of the present age of three individuals and sum of their ages. Let Chaintaya's age be $x$. Then Anil's age is 2$x$ (Since Anil's age is twice that of Chaitanya). Similarly, Advith's age is $x$+3. Since, sum of their ages is 63 2$x + x + x$+3 = 63
4$x$ = 60
$x$ = 15.
Advith's age = $x$+3 = 15 + 3 = 18
- Rashmi is 1/3rd the age of her father. In 13 years she will be half his age. What is Rashmi's present age?
- 15
- 9
- 15
- 13
Show the answer
Answer: 13
Let Rashmi's present age be $x$. Then, her father's age is 3$x$. In 13 years, Rashmi will be $x$+13 and her father will be 3$x$+13. Given, in 13 years Rashmi will be half her father's age. Hence,
$x$ + 13 = 1/2 x(3$x$+13)
1/2 $x$ = 13/2
$x$ = 13
Rashmi's present age = 13
- Sachin was as old as Ajith is at present at the time of his birth. If Sachin is currently 40 years old. How old is Ajith 5 years back?
- 15
- 20
- 25
- 12
Show the answer
Answer: 20
Let Ajith's present age be $x$. Then, Sachin's age at Ajith's birth is 40 - $x$ Given,
Sachin's age at Ajith's birth = Ajith's present age
40 -$x = x$
$x$ = 20
- The ratio of the age of father and son is 2 : 1. If the sum of their ages is 81. Find the difference in age of father and son.
- 29
- 25
- 36
- 27
Show the answer
Answer: 27
Let the age of father and son be 2$x$ and 1$x$ respectively.
Given, sum of their age is 81.
2$x + x$ = 81
$x$ = 27
Difference in the age of father and son = 2$x - x$ = 27
- Ratio of current age of A and B is 9:7. 2 years hence the ratio of their age will be 5 : 4. Find the present age of A.
- 18
- 14
- 16
- 12 km/hr
Show the answer
Answer: 18
Let current age of A and B be 9$x$ and 7$x$ respectively.
Ratio of their ages 2 years hence is 5:4.
i.e $\frac{9x + 2}{7x + 2} = \frac54$
36$x$ + 8 = 35$x$ + 10
$x$ = 2
Present age of A = 9x2 = 18
Present age of B = 7x2 = 14
- Sum of the ages of father and son three years ago is 40. Three years hence their age will be in the ratio 3:1. Find the ratio of their present age?
- 17 : 7
- 13 : 5
- 18 : 5
- 15 : 7
Show the answer
Answer: 13 : 5
After 3 years, let the age of father and son be 3$x$ and $x$ respectively.
Then present age will be 3$x$-3 and $x$-3
And, 3 years ago their age will be 3$x$-6 and $x$-6. The sum of which is equal to 40.
3$x$-6 + $x$-6 = 40
$x$ = 13
Father's present age : Son's present age = 3$x$-3 : $x$-3
= 3x13 - 3 : 13 - 3 = 36 : 10 = 18 : 5
- If 5 years from now, the ratio of age of A and B is 7:6 and 7 years ago their ratio was 3:2. Find their present age.
- 12 and 14
- 16 and 13
- 16 and 12
- 14 and 13
Show the answer
Answer: 16 and 13
Let the present age of A and B be $x$ and $y$ respectively.
Then, 5 years from now their age will be in the ratio:
$\frac{x + 5}{y + 5} = \frac{7}{6}$
6$x$ - 7$y$ = 5 _____ 1
7 years ago their age will be in ratio:
$\frac{x-7}{y-7} =\frac{3}{2}$
2$x$ - 3$y$ = -7 _____ 2
Solving 1 and 2, we get $x$ = 16 and $y$ = 13
The present age of A and B is 16 and 13 respectively
- If X is as much younger to Y as Y is younger to Z. Find the age of Y, if the sum of age of X and Z is 50.
- 10
- 15
- 20
- 25
Show the answer
Answer: 25
Let the age of X, Y and Z be $x, y$ and $z$ respectively.
Given,
$y - x = z - y$
2$y = x + z$
$y = \frac{x + z}{2}$
$x + z$ is given to be 50.
Therefore $y = \frac{50}{2}$ = 25
Hence Y is 25 years old.
- 10 years ago Ram’s father was 10 more than twice the age of Ram. 10 years hence sum of their ages will be 101. Find father’s present age.
- 18 seconds
- 10 seconds
- 9 seconds
- 5 seconds
Show the answer
Answer: 18 seconds
Let Ram's father's and Ram's present age be $x$ and $y$ respectively.
10 years ago, Ram's father was $x$ - 10 years old and and Ram was $y$ - 10 years old.
Given, $x$-10 = 10 + 2 ($y$-10)
$x - 2y$ = 0 => $x = 2y$ _____ 1
10 years hence, Ram's father will be $x$ + 10 years old and and Ram will $y$ + 10 years old.
Given,
$x$ + 10 + $y$+10 = 107
$x + y$ = 87
From 1, substituting $x$ = 2$y$
2$y + y$ = 87
$y$ = 29
Father's present age = 2x$y$ = 2x29 = 58 years
- If the ratio of A and B’s age is 4 : 3. What is B’s age 3 years hence, if A will be 35 years old in 3 years.
- 25
- 22
- 30
- 27
Show the answer
Answer: 27
Let the age of A and B be 4$x$ and 3$x$ respectively.
Given, A's age after 3 years = 35
Hence, 4$x$ + 3 = 35
$x$ = 8
B's age 3 years hence => 3$x$ + 3 = 27 years
- If the ratio of present ages of A, B and C is 3 : 5 : 7 and 4 years hence, the sum of their ages will be 72. Find the sum of the present ages of A, B and C.
- 55
- 60
- 67
- 75
Show the answer
Answer: 60
Let the present ages of A, B and C be 3$x$, 5$x$ and 7$x$ respectively.
Given 4 years hence, the sum of their ages is 72.
i.e 3$x$+4 + 5$x$+4 + 7$x$+4 = 72
15$x$ = 60.
$x$ = 4.
Sum of the present ages of A, B and C = 3$x$ + 5$x$ + 7$x$ = 12 + 20 + 28 = 60.
- Add 5 to Chaitanya’s age, divide it by 6 and multiply the result by 5, you will get his current age. Find Chai’s age 3 years before.
- 20 years
- 15 years
- 24 years
- 22 years
Show the answer
Answer: 22 years
Let Chaitanya's current age be $x$.
Given,
$\frac{x+5}{6}$ x 5 = $x$
5$x$ + 25 = 6$x$
$x$ = 25.
Chaitanya's age 3 years before = $x$ - 3 = 22 years.
- If the age of A and B is in ratio 5 : 7 and the product of two thirds of A’s age and three fourth’s of B’s age is 70, find A’s present age.
- 5 years
- 7 years
- 10 years
- 12 years
Show the answer
Answer: 10 years
Let ages of A and B be 5$x$ and 7$x$
Given,
$\frac{2}{3}$ (5$x$) x $\frac{3}{4}$(7$x$) = 70
$\frac{35 x^2}{2}$ = 70
$x^2$ = 4
x = 2
Hence the present age of A = 5x = 5x2 = 10 years.
