Problems on Ages: Types of problems, Tricks, Questions with Solutions
Saurav Sinha
| Updated: Apr 21, 2021 13:21 IST
In this article, we are going to cover the key concepts of problems on ages along with types of questions, tips and tricks and questions with solutions that will be beneficial for students in their exam preparation.
What are Problems on Ages?
Problems on ages are one of the applications of linear equations. When solving problems on ages, the ages of two or more persons are compared with the ratio, fraction or percentage. Then in that case, we could correlate the entire situation to the short tricks of ratio. The main challenge in handling the questions on problems on ages is your ability to bifurcate which data is of present and which one is of past and which one is of future.
Types of Questions from Problems on Ages
The types of questions from problems on ages asked in different government exams under aptitude section are as follows:
Ratio and Sum of Ages Given
If the ratio of present age of A and B is x : y and their sum of present age is P, then
A = x / (x+y) x P and B = y / (x+y) x P
Ratio and Product of Ages Given under Problems on Ages
In this type of age-related question, the ratio and the product of ages will be given. Candidates have to use those to conclude the final result.
Ratio of Present and Future Ages Given
In this type of age-related question, the ratio of present and future ages will be given. Candidates have to use those to conclude the final result.
Ratio of Past and Present Ages Given
In this type of age-related question, the ratio of past and present ages will be given. Candidates have to use those to conclude the final result.
Problems on Ages Tricks & Tips
Candidates can find different problems on ages tricks and tips from below for solving the questions.
Tip 1: If the current age is x, then n times the age is nx.
Tip 2:If the current age is x, then the age n years later/hence = x + n
Tip 3: If the current age is x, then age n years ago = x – n
Tip 4: The ages in a ratio a:b will be ax and bx
Tip 5: If the current age is x, then 1/n of the age is x/n
Once you’ve mastered Problems on Ages, you can attempt problems on ages MCQs.
Problems on Ages Questions with Solutions
Question 1: If the ratio of present age of Ashutosh and Vishal is 9 : 4 and their sum of present age is 52 years, find the present age of Vishal.
Solution: Let, age of Ashutosh be 9x and age of Vishal be 4x Then, sum of both ages = 9x + 4x = 13x
⇒ 13x = 52
⇒ x = 4 years
∴ Age of Vishal = 4x = 4 × 4 = 16 years
Question 2: Product of present age of Ram and Lakshaman is 2223 years and their present age ratio is 19:13 find the difference age of Ram and Lakshaman.
Solution: Let, age of Ram be 19x and age of Lakshaman be 13x Then, product of their ages = 19x × 13x = 247×2
⇒ 247×2 = 2223
⇒ x2 = 9
⇒ x = 3
Hence, required difference = 19x – 13x = 6x = 6 × 3 = 18 years
Question 3: The ratio of present age A and B is 13:10 after 2.5 years their ratio will be 32:25 then find the present age of A.
Solution: Let, present age of A = 13x and present age of B = 10x According to question:
(13x + 2.5)/(10x + 2.5) = 32/25
⇒ (13x + 2.5) × 25 = (10x + 2.5) × 32
⇒ 325x + 62.5 = 320x + 80
⇒ 5x = 17.5
⇒ x = 3.5
Question 4: If 5 years ago, the ratio of age of Mradul and Love was 1 : 2 and after 15 years from present their ratio would be 5 : 6. Find the age of Love after 20 years.
Solution: Let, present age of Mradul be x and present age of Love be y.
Then, according to question (x – 5)/(y – 5) = ½
⇒ 2x – 10 = y – 5
⇒ x = (y + 5)/2———- (1)
Also, (x + 15)/(y + 15) = 5/6
⇒ 6x + 90 = 5y + 75
⇒ 6x + 15 = 5y
Putting value of x from equation 1, we get 3y + 15 + 15 = 5y
⇒ 2y = 30
⇒ y = 15
∴ Age of Love after 20 years = 15 + 20 = 35 years.
Question 5: Ages of two persons differ by 16 years. If 6 year ago, the elder one be 3 times as old the younger one, find their present age?
Solution: Let the age of an younger person be A
age of elder person = (A + 16)
According to the question, we have
3(A – 6) = (A + 16 – 6)
⇒ 3A – 18 = A + 10
⇒ 2A = 28
⇒ A = 14
∴ The younger and elder person age is 14 years old and 30 years old.
Question 6: Twice the age of X is thrice the age of Y. 8 years back, the difference between the ages of X and Y was 18 years. What is the present age of X?
Solution: 2 times the age of X = 3 times the age of Y
Difference between X and Y, 8 years back = 18 years
2X = 3Y
⇒ X : Y = 3 : 2
Let the present age of X and Y be 3R and 2R respectively
⇒ 3R – 2R = 18
⇒ R = 18
⇒ 3R = 3 × 18 = 54
∴ The present age of X is 54 years
Question 7: A person’s age is 3 times the age of his friend. The total of their ages is 64 years. Find the ages of the person and his friend.
Solution: A person’s age is 3 times the age of his friend.
The total of their ages is 64 years.
Let the age of friend be x
Let the age of person be 4x
According to the question, we have
Total of their ages = x + 3x
Thus,
x + 3x = 64
4x = 64
x = 16
∴ The age of the friend = 16,
The age of the person = 16 × 3 = 48
∴ The age of the person and friend is 48 and 16 years.
Question 8: The mean of the ages of father and his son is 27 years. After 18 years, the father will be twice as old as his son. Their present ages are?
Solution: Let the ages of father and son be x and y respectively,
Then the mean ages of father and son be (x + y)/2,
According to the given conditions
(x + y)/2 = 27
⇒ (x + y) = 54
⇒ x + y = 54 —eqn (1)
After 18 years
x + 18 = 2(y + 18)
⇒ x + 18 = 2y + 36
⇒ x – 2y = 18 —eqn (2)
Solving equations 1 & 2 we get
x = 42 & y = 12
Hence, age of father is 42 and son is 12
Question 9: The ages of A, B and C together is 65 years. B is 2/3 of A and C is 9 years older than A. Then, what is the ratio of the respective age of C, A and B?
Solution: The ages of A, B and C together = 65
Let age of A = x
Age of C = x + 9
Age of B = 2x/3
Let the age of A be x years
The ages of A, B and C together = 65
According to the question,
⇒ x + x + 9 + 2x/3 = 65
⇒ (3x + 3x + 27 + 2x)/3 = 65
⇒ 8x + 27 = 65 × 3
⇒ 8x = 195 – 27
⇒ x = 168/8
⇒ x = 21
A’s age = 21
B’ age = 2x/3
⇒ 2 × 21/3
⇒ 14
C’ age = x + 9
⇒ 21 + 9
⇒ 30
The ratio of the respective age of C, A and B = 30 : 21 : 14
∴ The ratio of the respective age of C, A and B are 30 : 21 : 14.
Question 10: The present age of Ram is 5 times the age of his son. After 12 years the age of Ram will be twice the age of his son, find the present age of son.
Solution: Let the present age of ram and his son be R years and S years respectively.
R = 5S
R + 12 = 2 (S + 12)
Also, R + 12 = 2 (S + 12)
⇒ R = 2S + 12
Replacing R in terms of S we get,
5S = 2S + 12
⇒ S = 4 years
∴ the present age of son = 4 years.
Hence, (a) is the correct answer.
If you’ve learned Problems on Ages, you can move on to Simplification and Approximation concepts.
List of government exams where problems on ages questions are asked
Following is the list of government exams where problems on ages questions are asked under aptitude section.
- SBI PO, SBI Clerk, IBPS PO, IBPS Clerk
- SSC CGL, SSC CHSL, SSC MTS
- LIC AAO, LIC ADO
- RRB NTPC, RRB ALP
- UPSC
- MPSC
- KPSC
- BPSC
- WBPSC
- Other State-Level Recruitment Examinations
We hope you found this article informative and helpful regarding problems on ages, and please do not hesitate to contact us for any doubts or queries regarding the same. You can also download the Testbook App, which is absolutely free and start preparing for any government competitive examination by taking the mock tests before the examination to boost your preparation.
| If you are checking Problem of Ages article, also check the related maths articles in the table below: | |
| Find Roots of Quadratic Equation | Pie Diagram |
| Differential Calculus | Number Series |
| Linear Algebra | Time and Work |
Problems on Ages FAQs
Q.1 What is the Problems on Ages?
Ans.1 The Problems on Ages is purely based on your ability to handle the linear equation. There are some situations in which the ages of two or more persons are compared with the ratio, fraction or percentage.
Q.2 How many types of questions from problems on ages are there?
Ans.2 Important types of questions from problems on ages are: Ratio and Sum of Ages Given, Ratio and Product of Ages Given under Problems on Ages, Ratio of Present and Future Ages Given, Ratio of Past and Present Ages Given.
Q.3 Where I will find some of the sample questions related to problems on age?
Ans.3 We can find many questions with solutions in this problems on ages article.
Q.4 Questions from problems on ages come up in which government exams?
Ans.4 Problems on ages based questions come in various government examinations on a regular basis such as SBI PO, SBI Clerk, IBPS PO, IBPS Clerk, SSC CGL, SSC CHSL, SSC MTS, LIC AAO, LIC ADO, RRB NTPC, RRB ALP, UPSC, MPSC, KPSC, BPSC, WBPSC.
