Problems on Ages: Selected Quantitative Aptitude MCQs & Solutions

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Understanding the intricacies of age-related problems is crucial for honing mathematical skills and logical reasoning. This article will unravel strategies and tips to tackle age-related problems effectively, providing clarity and confidence in navigating such mathematical conundrums.

Basics of Problems On Age-Related Questions

To begin with, let us study the basics of problems on age-related questions:

Solving Equations

Age problems often involve solving equations to determine the ages of individuals. These equations typically require basic mathematical operations like addition, subtraction, multiplication, and division.

In addition to solving equations, logical reasoning plays a crucial role in age problems. You can deduce the unknown ages by analyzing the relationships between different individuals' ages based on the given information.

Formula to Solve Problems on Ages-Related Questions

Now, let us study the formula for solving problems on age-related questions:

Relative Age Difference

Understanding relative age differences is crucial in solving age problems. It helps compare the ages of two or more people.

Age-Related Problem Formula

A familiar formula used to solve age-related problems is the Age Difference Formula.

The formula is: Age Difference = Age of Person A - Age of Person B

For example, if Person A is 35 years old and Person B is 45 years old, the age difference would be:

Age Difference = 35 - 45= 10

Another formula, "Age = Current Year - Birth Year," is essential for quickly determining someone's age.

Types of Age-Related Questions & Examples 

Let us study how problems on age can be categorized into different types:

Present Ages

In aptitude tests, questions often revolve around determining an individual's age. These problems require applying basic arithmetic operations to calculate the present age based on given information.

Future and Past Ages

Another common type of age-related question involves calculating future or past ages. Solving these problems requires understanding how time affects one's age over different periods.

Tips & Tricks for Solving Ages Problems

Let us study some of the tips and tricks for solving age problems:

Break Down

Break down complex problems on age into smaller parts to simplify the process. By dividing the problem into manageable sections, it becomes easier to understand and solve it step by step.

Logical Reasoning

Applying logical reasoning is crucial in solving problems related to age. By critically analyzing the given information, you can eliminate unrealistic scenarios and focus on viable solutions more efficiently.

Click here for all related quantitative aptitude study resources that ensure quality over quantity to enhance and upgrade your skills.

Best MCQs on Problems on ages with solved answers

Here, we provide you with some of the best and most relevant sample questions of problems on age with solutions for you to practice and understand:

Question 1. Josy is three times as old as his son Tomar. In ten years, Josy will be twice as old as Tomar. How old are Josy and Tomar currently?

Solution: Let's denote Josy's current age as J and Tomar's current age as T.

Josy is three times as old as Tomar, represented as J = 3T

In ten years, Josy will be twice as old as Tomar. In ten years, Josy's age will be J + 10, and Tomar's age will be T + 10.

This can be represented as: J + 10 = 2(T + 10)

We have two equations:

1. J = 3T

2. J + 10 = 2(T + 10)

Substitute the value of J from the first equation into the second equation: 3T + 10 = 2(T + 10)

Expand and solve for T:

3T + 10 = 2T + 20

3T - 2T = 20 - 10

T = 10

Find Josy's age: Using the first equation J = 3T and substituting T = 10

J = 3(10)

J = 30

Josy is currently 30 years old, and Tomar is currently 10 years old.

Question 2: Five years ago, Sneha was three times as old as Priya. In ten years, Sneha will be twice as old as Priya. How old are Sneha and Priya currently?

Solution: Let's denote Sneha's current age as S and Priya's current age as P.

Five years ago, Sneha was three times as old as Priya. This can be represented as: S - 5 = 3(P - 5)

In ten years, Sneha will be twice as old as Priya. In ten years, Sneha's age will be S + 10, and Priya's age will be P + 10. This can be represented as: S + 10 = 2(P + 10)

We have two equations:

1. S - 5 = 3(P - 5)

2. S + 10 = 2(P + 10)

Let's start by solving the first equation for S:

S - 5 = 3(P - 5)

S = 3(P - 5) + 5

S = 3P - 15 + 5

S = 3P - 10

Now, substitute the value of S into the second equation:

3P - 10 + 10 = 2(P + 10)

3P = 2P + 20

3P - 2P = 20

P = 20

Now that we have found Priya's age, we can substitute P = 20 into one of the equations to find Sneha's age.

Let's use the equation S = 3P - 10

S = 3(20) - 10

S = 60 - 10

S = 50

Sneha and Priya are currently 50 and 20 years old, respectively.

Question 3: Arjun is currently three times as old as Kavita. In ten years, Arjun will be twice as old as Kavita. How old are Arjun and Kavita currently?

Solution: Let Arjun's current age be represented by A and Kavita's current age be represented by K.

Arjun is currently three times as old as Kavita. This can be represented as A = 3K

In ten years, Arjun will be twice as old as Kavita. This can be represented as: A + 10 = 2(K + 10)

We have two equations:

1. A = 3K

2. A + 10 = 2(K + 10)

Let's substitute the value of A from the first equation into the second equation: 3K + 10 = 2(K + 10)

Now, let's solve for K:

3K + 10 = 2K + 20

3K - 2K = 20 - 10

K = 10

Now that we have found Kavita's age, we can substitute K = 10 into the first equation to find Arjun's age:

A = 3(10)

A = 30

Arjun is currently 30 years old, and Kavita is currently 10 years old.

Question 4: Mohan is 2 years older than Kapil, who is twice as old as Pillai. If the total ages of Mohan, Kapil, and Pillai are 27, then how old is Kapil?

Solution: Let's denote Mohan's age as M, Kapil's age as K, and Pillai's age as P.

Mohan is 2 years older than Kapil. This can be represented as M=K+2

Kapil is twice as old as Pillai. This can be represented as K=2P

The total of their ages is 27. This can be represented as M+K+P=27

We have three equations:

1. M=K+2

2. K=2P

3. M+K+P=27

Let's use the second equation to express K in terms of P: K=2P

Now, substitute this expression for K into the first and third equations: M=(2P)+2 [from equation 1]

M+(2P)+P=27 [from equation 3]

Simplify the equations:

1. M=2P+2

2. M+3P=27

Now, let's substitute the expression for M from equation 1 into equation 2:

2P+2+3P=27

5P+2=27

5P=25

P=5

Now that we have found P, which represents Pillai's age, we can use equation 2 to find Kapil's age: K=2P

K=2×5

K=10

Check the solution if our solution satisfies all the conditions given in the problem statement:

Mohan is 2 years older than Kapil:

M=K+2

M=10+2=12

Kapil is twice as old as Pillai:

K=2P

10=2×5

The total of their ages is 27:

M+K+P=27

12+10+5=27

Kapil is 10 years old.

Question 5: The sum of the ages of a son and father is 56 years; after four years, the age of the father will be three times that of the son. What is the age of the son and the father, respectively?

Solution: Let's denote the son's current age as S and the father's age as F.

The sum of the ages of the son and father is 56 years: S+F=56

After four years, the age of the father will be three times that of the son: (F+4)=3(S+4)

We have two equations:

1. S+F=56

2. (F+4)=3(S+4)

Let's simplify the second equation:

F+4=3S+12

F=3S+8

Now, substitute the expression for F from the second equation into the first equation:

S+(3S+8)=56

Now, solve for S:

4S+8=56

4S=56−8

4S=48

S=12

Now that we have found the age of the son, we can substitute S=12 into one of the equations to find the age of the father. 

Let's use the first equation:

12+F=56

F=56−12

F=44

After four years, the age of the father will be three times that of the son:

(44+4)=3(12+4)

48=3×16

48=48

The son is 12 years old, and the father is 44 years old.

Question 6: Asha's father was 38 years of age when she was born, while her mother was 36 years old when her brother, four years younger than her, was born. What is the difference between the ages of her parents?

Solution: Let's calculate the current ages of Asha's parents.

Asha's father was 38 years old when Asha was born. So, if Asha is currently x years old, then Asha's father is currently 38+x years old.

Asha's mother was 36 years old when her brother, who is four years younger than her, was born. So, if Asha's brother is currently y years old, then Asha's mother is currently 36+y years old.

Now, since Asha's brother is four years younger than her, we have y=x−4.

So, Asha's mother's current age can be expressed as x as 36+(x−4)=32+x.

Now, we have the current ages of both parents as functions of x:

• Asha's father: 38+x

• Asha's mother: 32+x

To find the difference between their ages, we subtract:

(38+x)−(32+x)

38+x−32−x

38−32=6

So, the difference between the ages of Asha's parents is 6 years.

Question 7: What is the minimum age a father must have been when his son was born if he wants to ensure that he will be twice his son's age when his son turns 30?

Solution: The father wants to be twice his son's age when the son turns 30.

Let's denote the age of the father when the son was born as F (in years).

The age of the son when he turns 30 is 30 years.

At the time the son turns 30, the father should be twice the son's age.

We can write the equation as F+30=2×30.

Let's solve the equation:

F+30=60.

Subtract 30 from both sides:

F+30-30=60−30

F=30

The father must have been 30 years old when his son was born to ensure that he will be twice his son's age when he turns 30.

Question 8: Manju is currently twice the age of her sister, Mina. Six years ago, Manju was three times as old as Mina. How old are Manju and Mina now?

Solution: Manju's current age is twice the age of her sister Mina. Six years ago, Manju was three times as old as Mina.

Let's denote Manju's current age as M and Mina's current age as A.

Manju's current age is twice the age of her sister Mina: M=2A.

Six years ago, Manju was three times as old as Mina: M−6=3(A−6).

• We have two equations:

• M=2A (Equation 1)

• M−6=3(A−6) (Equation 2)

• Substitute the value of M from equation 1 into equation 2:

• 2A−6=3(A−6) 2

• 2A−6=3A−18

Rearrange the equation:

2A−3A=−18+6

−A=−12

A=12

Calculate Manju's age using

M=2A

M=2×12

M=24

Manju is currently 24 years old, and Mina is currently 12 years old.

Question 9: At present, Meera is three times the age of her younger sister, Radha. Six years ago, Meera was five times as old as Radha. How old are Meera and Radha now?

Solution: Let's denote Meera's current age as M and Radha's current age as R.

Meera's current age is three times the age of Radha: M=3R.

Six years ago, Meera was five times as old as Radha: M−6=5(R−6).

We have two equations:

M=3R -(1)

M−6=5(R−6) -(2)

Substitute the value of M from equation 1 into equation 2:

3R−6=5(R−6)

3R−6=5R−30

Rearrange the equation:

3R−5R=−30+6

−2R=−24

R=12

Calculate Meera's age using M=3R

M=3×12

M=36

Meera is currently 36 years old, and Radha is currently 12 years old.

Question 10: Sarah is currently 4 times as old as her daughter. In 10 years, Sarah will be twice as old as her daughter. How old are Sarah and her daughter currently?

Solution: Let's denote Sarah's current age as S and Sarah's daughter's current age as D.

According to the problem, Sarah is currently 4 times as old as her daughter: S = 4 × D

In 10 years, Sarah will be twice as old as her daughter: (S + 10) = 2 × (D + 10)

Now, we have a system of two equations:

Equation 1: S = 4 × D

Equation 2: (S + 10) = 2 × (D + 10)

First, let's use Equation 1 to express Sarah's age (S) in terms of her daughter's age (D): S = 4 × D

Now, we'll substitute this expression for S into Equation 2: 

(4 × D + 10) = 2 × (D + 10)

Expanding the equation:

4D + 10 = 2D + 20

2D=10

D=5

So, Sarah's daughter is currently 5 years old.

Now, let's find Sarah's current age (S) using Equation 1:

S = 4 × D

S = 4× 5

S = 20

So, Sarah is currently 20 years old.

Sarah is 20 years old, and her daughter is 5 years old.

Conclusion

Mastering age-related problems is crucial for acing aptitude tests, especially those for government exams. Understanding the key concepts, formulas, and strategies discussed can significantly boost your problem-solving skills.

By practising sample problems and honing your abilities, you're gearing up to tackle any age-related question that comes your way in these exams. Remember, practice makes perfect!

Frequently Asked Questions (FAQs)   

1. What are age problems in aptitude tests?

Age problems in aptitude tests involve determining the age of individuals based on given conditions like birth dates, events, or relationships.

2. How can mastering age problems benefit me for government exams?

Mastering age problems enhances your problem-solving skills and analytical thinking, which are crucial for scoring well in government exams that often feature such questions.

3. Why are key concepts and formulas important for solving age-related questions?

Understanding key concepts and formulas simplifies the process of solving complex age-related questions efficiently within a limited time frame during aptitude tests.

4. How can strategies and tricks help in solving age problems effectively?

Strategies and tricks provide shortcuts and techniques to approach different types of age-related questions quickly, improving accuracy and saving time during exams.

5. Where can I find sample practice problems on ages with solutions?

Sample practice problems for different ages with solutions are available online or in study materials specific to aptitude test preparation, helping you practice extensively before exams.

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