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Age Problems - Advanced Level: comparative ages ADVANCED

Master age problems concepts through this hard problem set practice set. Worksheet 26 of 30 contains 20 advanced-level problems. Deep dive into comparative ages while learning age ratios, age differences, sum of ages. Recommended for advanced learners aiming for complex scenarios and multi-step problems.

📝 Worksheet 26 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
Your progress through Age Problems
Worksheet 26 of 30 (86% complete)

Question 1

A is 7 years older than B. A's age equals the cost price (₹100) and B's age equals the selling price when profit is 26%. Find A's age.
Given: A = cost price = 100, B = selling price = 126. Age difference matches: 100 - 126 = -26
integrated, multi_topic

Question 2

10 years ago, A was half as old as B. In 5 years, what will be the age difference between B and A?
10 years ago: A was 12, B was 14. Check: 12 = ½ × 14 ✓
Present ages: A = 22, B = 24
In 5 years: A = 27, B = 29
Age difference = |29 - 27| = 2
(Age difference stays constant over time = B - A = 2)
chronological_chain

Question 3

In 4 years, Thomas will be twice as old as Omkar was 3 years ago. If Omkar is 18 now, how old is Thomas now?
In 4 years: Thomas=Thomas(now)+4, Omkar was 18-3=15 three years ago. Thomas(now)+4=2*15 => Thomas(now) = 2*15 - 4 = 26.
reverse

Question 4

William is 14, Hazel is 18. After 3 years, what is the ratio of their ages?
William: Hazel = 17:21, after 3 years.
future_ratio

Question 5

Colton and Madison together are 27. If Colton is 12, what is Madison's age?
Madison = 27 - 12 = 15
sum

Question 6

Family: Connor, Emily, Vidhi, Allison. Average age is 12. What is the sum of ages?
Total = 12*4 = 48
average

Question 7

The sum of A and B's ages is 54. Twice A's age minus B's age is 21. Find A's age.
A + B = 54
2A - B = 21
Adding the two equations: (A + B) + (2A - B) = 54 + 21
3A = 75
A = 25
Verification: B = 54 - 25 = 29
2(25) - 29 = 21 = 21 ✓
equation

Question 8

Priya is 16, Anup is 20. After 8 years, what is the ratio of their ages?
Priya: Anup = 24:28, after 8 years.
future_ratio

Question 9

In 2024, the Rishabh family consists of: - Rishabh (Father): 47 years - Sienna (Mother): 42 years - Calvin (Son): 22 years - Sameer (Daughter): 18 years Additional information: • Father is 4 times as old as daughter was 5 years ago • Mother was 25 years old when son was born • In 5 years, sum of all ages will be 149 Based on the relationships, what is Calvin's current age?
From given relationships, Calvin's age = 22
case_study, comprehensive

Question 10

Present ages of Harper, Vrijesh, Kabir are in ratio 2:3:4. Sum of ages is 54. Find Harper's age.
Let ages be 2x, 3x, 4x. Sum = 9x = 54, so x = 6. Harper = 2×6 = 12
complex_ratio

Question 11

10 years ago, A was half as old as B. In 5 years, what will be the age difference between B and A?
10 years ago: A was 12, B was 14. Check: 12 = ½ × 14 ✓
Present ages: A = 22, B = 24
In 5 years: A = 27, B = 29
Age difference = |29 - 27| = 2
(Age difference stays constant over time = B - A = 2)
chronological_chain

Question 12

A is 14. What is (A+7) and (2A-4)? What is the value of (A+7)?
A+7=21; 2A-4=24
olympiad_expression

Question 13

The sum of ages of all family members is 124 and their average age is 31. How many members are there in the family?
number = total / average = 124 / 31 = 4
member_count

Question 14

The average age of a group is 14. The sum of their ages is 84. How many people are there in the group?
Count = sum / average = 84 / 14 = 6
group_size

Question 15

The average age of a group is 27. The sum of their ages is 135. How many people are there in the group?
Count = sum / average = 135 / 27 = 5
group_size

Question 16

A is 4 years older than B. If B is 12 and A is 10, is the data correct?
If B is 12, A should be 16. But A is 10. Data is inconsistent.
contradiction

Question 17

Prem is 14, Shravan is 14. After 6 years, what is the ratio of their ages?
Prem: Shravan = 20:20, after 6 years.
future_ratio

Question 18

Grandfather is 70 years old, his son is 47 years old, and his grandson is 27 years old. What is the sum of their ages?
Sum = 70 + 47 + 27 = 144
family_tree

Question 19

In 4 years, Vishal will be twice as old as Freya was 3 years ago. If Freya is 18 now, how old is Vishal now?
In 4 years: Vishal=Vishal(now)+4, Freya was 18-3=15 three years ago. Vishal(now)+4=2*15 => Vishal(now) = 2*15 - 4 = 26.
reverse

Question 20

A is 4 years older than B. If B is 8 and A is 6, is the data correct?
If B is 8, A should be 12. But A is 6. Data is inconsistent.
contradiction
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