Problems on Ages: Mastering Competitive Exam Concepts

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Problems on Ages

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Problems on Ages MCQ & Objective Questions

Understanding "Problems on Ages" is crucial for students preparing for various school and competitive exams. This topic not only enhances your problem-solving skills but also boosts your confidence in tackling age-related questions. Practicing MCQs and objective questions on this topic can significantly improve your exam performance and help you score better. With a focus on important questions and practice questions, you can master this essential area of mathematics.

What You Will Practise Here

Basic concepts of age problems and their formulations
Solving age-related equations using algebraic methods
Understanding the relationship between ages of individuals
Application of ratios and proportions in age problems
Common age problem scenarios and their solutions
Practice with real-life examples and word problems
Tips and tricks for quick calculations and problem-solving

Exam Relevance

"Problems on Ages" is a recurring topic in CBSE, State Boards, and competitive exams like NEET and JEE. Students can expect questions that require them to determine the ages of individuals based on given conditions. Common question patterns include direct age calculations, age comparisons, and problems involving multiple individuals. Mastering this topic will not only prepare you for school exams but also give you an edge in competitive assessments.

Common Mistakes Students Make

Misinterpreting the relationships between ages in word problems
Neglecting to set up equations correctly based on the problem statement
Overlooking the importance of units and time frames in age calculations
Failing to check the feasibility of the calculated ages
Rushing through calculations, leading to simple arithmetic errors

FAQs

Question: What are some effective strategies for solving age problems?
Answer: Break down the problem into smaller parts, set up equations based on the relationships given, and solve step by step.

Question: How can I improve my speed in solving age-related MCQs?
Answer: Practice regularly with timed quizzes and focus on understanding the concepts rather than memorizing solutions.

Start your journey towards mastering "Problems on Ages" today! Solve practice MCQs and test your understanding to ensure you are well-prepared for your exams. Your success is just a question away!

Q. The age of a father is twice the age of his son. If the sum of their ages is 60 years, how old is the son?

A. 20
B. 25
C. 30
D. 15

Solution

Let the son's age be x. Then the father's age is 2x. The equation is x + 2x = 60, which simplifies to 3x = 60, so x = 20.

Correct Answer: B — 25

Q. The age of a grandfather is 3 times the age of his grandson. If the grandfather is 60 years old, how old is the grandson?

A. 15
B. 20
C. 25
D. 30

Solution

If the grandfather is 60 years old, then the grandson is 60 / 3 = 20 years old.

Correct Answer: B — 20

Q. The age of a grandfather is 3 times the age of his grandson. If the grandson is 15 years old, how old is the grandfather?

A. 30
B. 45
C. 60
D. 75

Solution

If the grandson is 15 years old, then the grandfather is 3 * 15 = 45 years old.

Correct Answer: C — 60

Q. The age of a grandfather is 4 times the age of his grandson. If the grandson is 8 years old, how old is the grandfather?

A. 24
B. 32
C. 36
D. 40

Solution

If the grandson is 8 years old, then the grandfather is 4 * 8 = 32 years old.

Correct Answer: B — 32

Q. The age of a grandfather is 4 times the age of his grandson. If the grandson is 8 years old, what is the grandfather's age?

A. 24
B. 32
C. 36
D. 40

Solution

If the grandson is 8 years old, then the grandfather is 4 * 8 = 32 years old.

Correct Answer: B — 32

Q. The age of a grandfather is 60 years and the age of his grandson is 15 years. What is the ratio of their ages?

A. 4:1
B. 5:1
C. 6:1
D. 7:1

Solution

The ratio of their ages is 60:15, which simplifies to 4:1.

Correct Answer: B — 5:1

Q. The age of a grandfather is three times the age of his grandson. If the grandson is 12 years old, what is the grandfather's age?

A. 30
B. 36
C. 40
D. 42

Solution

If the grandson is 12, then the grandfather is 3 * 12 = 36 years old.

Correct Answer: B — 36

Q. The age of a man is 5 years more than twice the age of his son. If the son is 10 years old, how old is the man?

A. 20
B. 25
C. 30
D. 35

Solution

If the son is 10 years old, then the man's age is 2 * 10 + 5 = 25 years.

Correct Answer: C — 30

Q. The age of a mother is 4 times that of her daughter. If the daughter is 8 years old, what is the mother's age?

A. 24
B. 32
C. 36
D. 40

Solution

If the daughter is 8 years old, then the mother is 4 * 8 = 32 years old.

Correct Answer: A — 24

Q. The age of a mother is 4 times the age of her daughter. If the daughter is 5 years old, how old is the mother?

A. 15
B. 20
C. 25
D. 30

Solution

If the daughter is 5 years old, then the mother is 4 * 5 = 20 years old.

Correct Answer: B — 20

Q. The age of a mother is 4 times the age of her daughter. If the daughter is 6 years old, how old is the mother?

A. 18
B. 20
C. 24
D. 30

Solution

If the daughter is 6 years old, then the mother is 4 * 6 = 24 years old.

Correct Answer: C — 24

Q. The age of a mother is 5 times the age of her daughter. If the daughter is 6 years old, what is the mother's age?

A. 24
B. 30
C. 36
D. 40

Solution

If the daughter is 6 years old, then the mother is 5 * 6 = 30 years old.

Correct Answer: A — 24

Q. The age of I is three times the age of J. If the difference in their ages is 24 years, how old is J?

A. 8
B. 12
C. 16
D. 20

Solution

Let J's age be x. Then I's age is 3x. The difference is 3x - x = 24, hence 2x = 24, x = 12. Therefore, J is 12 years old.

Correct Answer: C — 16

Q. The ages of M and N are in the ratio 5:3. If the sum of their ages is 64 years, what is M's age?

A. 30
B. 32
C. 34
D. 36

Solution

Let M's age be 5x and N's age be 3x. Then 5x + 3x = 64. Solving gives x = 8, thus M = 40.

Correct Answer: B — 32

Q. The ages of O and P are in the ratio 5:3. If the sum of their ages is 64 years, what is O's age?

A. 30
B. 32
C. 40
D. 42

Solution

Let O's age be 5x and P's age be 3x. Then 5x + 3x = 64. Solving gives x = 8, hence O = 40.

Correct Answer: B — 32

Q. The ages of O and P are in the ratio 5:3. If the sum of their ages is 64, what is O's age?

A. 40
B. 32
C. 36
D. 28

Solution

Let O's age be 5x and P's age be 3x. Then, 5x + 3x = 64. Solving gives x = 8, O's age = 5 * 8 = 40.

Correct Answer: A — 40

Q. The ages of two friends are in the ratio 3:5. If the sum of their ages is 40 years, what is the age of the older friend?

A. 15
B. 20
C. 25
D. 30

Solution

Let the ages be 3x and 5x. Then, 3x + 5x = 40, so 8x = 40, x = 5. The older friend is 5 * 5 = 25 years old.

Correct Answer: C — 25

Q. The ages of two friends are in the ratio 3:5. If the sum of their ages is 40 years, what is the age of the younger friend?

A. 12
B. 15
C. 18
D. 20

Solution

Let the ages be 3x and 5x. Then, 3x + 5x = 40, so 8x = 40, x = 5. The younger friend's age is 3x = 15 years.

Correct Answer: B — 15

Q. The ages of two siblings are in the ratio 3:5. If the younger sibling is 9 years old, how old is the older sibling?

A. 15
B. 18
C. 20
D. 25

Solution

If the younger sibling is 9 years old, then the older sibling is (5/3) * 9 = 15 years old.

Correct Answer: B — 18

Q. The combined age of O and P is 80 years. If O is 10 years older than P, how old is O?

A. 35
B. 40
C. 45
D. 50

Solution

Let P's age be x. Then O's age is x + 10. So, x + (x + 10) = 80. Solving gives x = 35, hence O = 45.

Correct Answer: B — 40

Q. The present age of a grandfather is 4 times that of his grandson. If the grandson is 5 years old, what is the grandfather's age?

A. 15
B. 20
C. 25
D. 30

Solution

If the grandson is 5 years old, then the grandfather is 4 * 5 = 20 years old.

Correct Answer: D — 30

Q. The ratio of the ages of G and H is 3:2. If G is 30 years old, how old is H?

A. 20
B. 25
C. 30
D. 35

Solution

If G is 30 years old, then H's age is (2/3) * 30 = 20 years.

Correct Answer: A — 20

Q. The ratio of the ages of G and H is 3:4. If H is 32 years old, how old is G?

A. 24
B. 30
C. 28
D. 20

Solution

If H is 32 years, then G's age = (3/4) * 32 = 24 years.

Correct Answer: A — 24

Q. The ratio of the ages of I and J is 3:4. If the sum of their ages is 70 years, what is I's age?

A. 30
B. 35
C. 40
D. 45

Solution

Let I's age be 3x and J's age be 4x. Then 3x + 4x = 70. Solving gives x = 10, hence I = 30.

Correct Answer: B — 35

Q. The sum of the ages of A and B is 50 years. If A is 10 years older than B, how old is A?

A. 20
B. 25
C. 30
D. 35

Solution

Let B's age be x. Then A's age is x + 10. So, x + (x + 10) = 50. Solving gives x = 20, hence A = 30.

Correct Answer: C — 30

Q. The sum of the ages of A and B is 50 years. If A is 10 years older than B, what is B's age?

A. 20
B. 25
C. 30
D. 15

Solution

Let B's age be x. Then A's age is x + 10. So, x + (x + 10) = 50. Solving gives x = 20.

Correct Answer: B — 25

Q. The sum of the ages of a father and his son is 50 years. If the father is 30 years older than the son, how old is the son?

A. 10
B. 15
C. 20
D. 25

Solution

Let the son's age be x. Then the father's age is x + 30. So, x + (x + 30) = 50. Solving gives x = 10.

Correct Answer: C — 20

Q. The sum of the ages of a father and his son is 50 years. If the father is 40 years old, how old is the son?

A. 10
B. 15
C. 20
D. 30

Solution

If the father is 40 years old, then the son is 50 - 40 = 10 years old.

Correct Answer: C — 20

Q. The sum of the ages of a mother and her daughter is 50 years. If the mother is 4 times as old as her daughter, how old is the daughter?

A. 10
B. 8
C. 12
D. 6

Solution

Let the daughter's age be x. Then the mother's age is 4x. The equation is x + 4x = 50, which simplifies to 5x = 50, so x = 10.

Correct Answer: A — 10

Q. The sum of the ages of a mother and her daughter is 60 years. If the daughter is 15 years old, how old is the mother?

A. 35
B. 40
C. 45
D. 50

Solution

If the daughter is 15 years old, then the mother is 60 - 15 = 45 years old.

Correct Answer: B — 40

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