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# Problem On Ages Questions ## Definition of Problem On Ages

Problems on ages are a type of word problem based on algebra, which deals with the current, past, and future age of people. It can be further categorized into three forms, i.e. Questions for determining the present age, Questions for calculating the age of person after particular years, and questions that calculate the age of a person before given years. Moreover, these types of questions cover cases of different types with various combinations of ratios and fractions.

### Important Statements and Equations:

• If the present age is given as p, then q times the present age = ‘qp’
• If the present age is given as p, then age q years later/hence = p + q
• If the present age is given as p, then age q years ago = p – q.
• The age is given in the ratio p: q, then the age will be px and qx.
• If the present age is given as p, then 1/qth of the age is p/q.

### Common Expressions

Below given are some of the frequent expressions that should be remembered while solving the problems on ages. In all the given expression, we assume x as the present age of a man.
• Man’s age five years hence or from now = (x + 5)
• Man’s age six years ago = (x – 6)
• The woman is four times as old as man= (Woman’s age : 4x)
• The woman is thrice as old as man five years ago = (Woman’s age : 3(x-5))

### Rules

• It is essential to categorize the key expressions and arrange the information by assigning different variables to various unknown quantities in order to acquire the correct answer.
• Translate the given problem into algebraic equations with the help of variables and phrases which represent the problems.
• Select only one variable to solve the problem.
• Use methods such as elimination and matrix to solve the equations.
• If the information in the question comprises ages at different points of time, assume the present age as ‘x.’
• If the information in the question comprises ages of different people, assume the age of the youngest person as ‘x.’
• Read the question very carefully. The phrase ‘n time more than,’ ‘after x years,’ and ‘before x years’ needs to be understood correctly.
• Check the obtained answer, both mathematically and intuitively.

Question 1 Time: 00:00:00
Max is one-third of his mother’s age. After 6 years, Max’s would be 2 12 Of Max’s age. How many times Max’s mother would be further 6 years hence? 3.57

3.57

2.56

2.56

3.11

3.11

2.0

2.0

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Question 2 Time: 00:00:00
4 children are born at intervals of 2 years. On adding their ages, we get the sum 40 years. How old is the eldest child? 11

11

13

13

16.5

16.5

21

21

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Question 3 Time: 00:00:00
6 children are born, each at an interval of 1.5 years. On adding the ages of all the 6 children, we get the sum as 60. How old is the youngest child? 7

7

8.5

8.5

5

5

6.25

6.25

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Question 4 Time: 00:00:00
Ross’s age is 2 times more than his friend Sam’s age. 12 years hence, his age bill be 32 Times more than that of Sam. Determine how many times more the age of Ross will be further after 12 years. One and a half times

One and a half times

Two times

Two times

Two and a half time

Two and a half time

Three-time

Three-time

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Question 5 Time: 00:00:00
Samantha told her office colleague Monika that when she was born, Samantha was as old as Monika’s present age.” If Samantha’s current age is 36, how old was Monika 4 years ago? 14

14

12

12

18

18

21

21

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Question 6 Time: 00:00:00
A father said to his daughter Amma, “At the time of your birth, I was double of your present age.” If the daughter’s age at present is 15 years, identify What the father’s age 5 years later? 41

41

48

48

51

51

50

50

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Question 7 Time: 00:00:00
A father was twice the age of his son Jack 5 years ago, and 7 years; hence, Jack would be one-third of his father. Find in what ratio is their current age. 29:53

29:53

29:53

29:53

54:30

54:30

30:54

30:54

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Question 8 Time: 00:00:00
Ross is 8 years younger than Luke. Their ages are in the proportion of 4:6. Calculate the present age of Ross? 18

18

24

24

20

20

16

16

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Question 9 Time: 00:00:00
Ashley and Dennis’s present age is in the proportion of 5:3. If the proportion of Ashley’s age 3 years back and Dennis’s age 3 years later would be 1:1. Calculate the proportion of Ashley’s age after 3 years and Dennis’s age three years before. 3:1

3:1

2:1

2:1

22:11

22:11

13:6

13:6

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Question 10 Time: 00:00:00
Saif is one-fifth years old than his mother. After three years, his mother’s age will be four times that of Saif. How old would Saif’s mother be 3 years hence? 22

22

32

32

33

33

43

43

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Question 11 Time: 00:00:00
Alex is 10 years elder to Rachel. If Alex’s age was 3 times the age of Rachel 4 years prior, then find Alex’s age after one year. 20

20

21

21

39

39

27

27

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