Age-Based Puzzles - Advanced Level: past ages
ADVANCED
Master age-based puzzles concepts through this hard problem set practice set. Worksheet 26 of 30 contains 20 advanced-level problems. Deep dive into past ages while learning age relationships, age-based logic, family ages. Recommended for advanced learners aiming for complex scenarios and multi-step problems.
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Worksheet 26 of 30 (86% complete)
Question 1
The product of the ages of Isaac and Kaushal is 84, and the sum of their ages is 19. Find Isaac's age.
Let ages be x and y. xy = 84 x + y = 19 Solving gives x = 7, y = 12 Therefore, Isaac's age = 12
Question 2
When Veena was born, Omkar was 18 years old. The sum of their present ages is 76. Find Veena's age when Veena was half of Omkar's age (this will happen 11 years ago).
Let Veena's current age = 29, Omkar's current age = 47 Given: When Veena was born (0 years old), Omkar was 18 years old. Therefore, Omkar is always 18 years older than Veena. So 47 = 29 + 18 ✓
Condition: Find t such that Veena's age = ½ of Omkar's age Equation: 29 + t = ½(47 + t) Multiply both sides by 2: 229 + 2t = 47 + t Simplify: 229 + 2t - t = 47 229 + t = 47 t = 47 - 229 t = 47 - 58 = -11
At that time, Veena's age = 29 + -11 = 18 Verification: When Veena is 18, Omkar is 36 = 36 Check: Is 18 = ½ × 36? ½ × 36 = 18.0 ✓
Note: Mathematically, this always equals the age difference (18) because: event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff
Question 3
Four people: Andrew, Tyler, Mahesh, Jaxson
Given:
1. The sum of all four ages is 123
2. Andrew + Tyler = 52
3. Jaxson is 3 years older than Mahesh
4. Andrew is 22 years old
Find Jaxson's age.
Step 1: From clue 4, Andrew = 22
Step 2: Using clue 2, we can find the other person in that pair
Step 3: Using clue 3 and clue 1, we can determine all ages
Tournament participants: Tanu, Bennett, Charlotte, Shivani
Given the following clues:
1. Tanu is younger than Bennett
2. Bennett is younger than Charlotte
3. Charlotte is younger than Shivani
4. Each person is exactly 5 years older than the person immediately younger than them.
5. Shivani is 36 years old.
Determine Charlotte's age.
Step 1: From clues 1-3, the age order from youngest to oldest is: Tanu → Bennett → Charlotte → Shivani
Step 2: From clue 4, each consecutive person differs by exactly 5 years. So if youngest = x, then: Tanu=x, Bennett=x+5, Charlotte=x+10, Shivani=x+15
Step 3: From clue 5, Shivani (the 4th (oldest)) = 36 Therefore, x + 15 = 36 Solving: x = 36 - 15 = 21
Step 5: Charlotte is the 3rd. Therefore, Charlotte = 31
Question 5
Om is half as old as Eleanor was when Om was 16 years old. If Eleanor is now 53 years old, find Om's current age.
When Om was 16 years old, that was 17 years ago At that time, Eleanor was 53 - 17 = 36 years old Now Om is half of 36 Therefore, Om's current age = 36 ÷ 2 = 18
Question 6
When Delilah was born, Vandana was 21 years old. The sum of their present ages is 37. Find Delilah's age when Delilah was half of Vandana's age (this will happen in 13 years).
Let Delilah's current age = 8, Vandana's current age = 29 Given: When Delilah was born (0 years old), Vandana was 21 years old. Therefore, Vandana is always 21 years older than Delilah. So 29 = 8 + 21 ✓
Condition: Find t such that Delilah's age = ½ of Vandana's age Equation: 8 + t = ½(29 + t) Multiply both sides by 2: 28 + 2t = 29 + t Simplify: 28 + 2t - t = 29 28 + t = 29 t = 29 - 28 t = 29 - 16 = 13
At that time, Delilah's age = 8 + 13 = 21 Verification: When Delilah is 21, Vandana is 42 = 42 Check: Is 21 = ½ × 42? ½ × 42 = 21.0 ✓
Note: Mathematically, this always equals the age difference (21) because: event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff
Question 7
Ankur is 25 years older than John and is now 43 years old. How old was Ankur 14 years ago?
Current age of Ankur = 43 14 years ago = 43 - 14 = 29
Question 8
Tournament participants: Anjali, Purvi, Dhruv, Rylee
Given the following clues:
1. Anjali is younger than Purvi
2. Purvi is younger than Dhruv
3. Dhruv is younger than Rylee
4. Each person is exactly 3 years older than the person immediately younger than them.
5. Purvi is 25 years old.
Determine Dhruv's age.
Step 1: From clues 1-3, the age order from youngest to oldest is: Anjali → Purvi → Dhruv → Rylee
Step 2: From clue 4, each consecutive person differs by exactly 3 years. So if youngest = x, then: Anjali=x, Purvi=x+3, Dhruv=x+6, Rylee=x+9
Step 3: From clue 5, Purvi (the 2nd) = 25 Therefore, x + 3 = 25 Solving: x = 25 - 3 = 22
The average age of 5 people is 34. If Ishaan (age 32) leaves and a new person joins, the average becomes 41. Find the age of the new person.
Initial total = 34 × 5 = 170 After Ishaan leaves: 170 - 32 = 138 New total = 41 × 5 = 205 New person's age = 205 - (138) = 67
Question 10
The sum of ages of Thomas, Sanjit, and Mridul is 21. Their ages are in the ratio 1:4:2. How old is Mridul?
Sum of ratios = 1 + 4 + 2 = 7 Each unit = 21 ÷ 7 = 3 Mridul's ratio = 2 Age = 2 × 3 = 6
Question 11
Hardik is half as old as Navya was when Hardik was 19 years old. If Navya is now 46 years old, find Hardik's current age.
When Hardik was 19 years old, that was 16 years ago At that time, Navya was 46 - 16 = 30 years old Now Hardik is half of 30 Therefore, Hardik's current age = 30 ÷ 2 = 15
Question 12
The sum of ages of Manmohan, Camila, and Sanjana is 49. Their ages are in the ratio 4:1:2. How old is Manmohan?
Sum of ratios = 4 + 1 + 2 = 7 Each unit = 49 ÷ 7 = 7 Manmohan's ratio = 4 Age = 4 × 7 = 28
Question 13
Currently, Urvi is 4/9 of Audrey's age. After 12 years, Urvi will be 1/2 of Audrey's age. Find Urvi's present age.
Let Audrey = x, then Urvi = 4/9x After 12 years: 4/9x + 12 = 1/2(x + 12) Solving gives x = 81, so Urvi = 36
Question 14
If Jyoti were 7 years younger, she would be 4/11 of Samuel's age 9 years from now. If Jyoti is 7 years younger than Samuel, find Jyoti's present age.
Let Samuel = 49, then Jyoti = 42 Check: (42 - 7) = 4/11 × (49 + 9) 35 = 4/11 × 58 ✓
Question 15
Sakshi is 6 years older than Sarvesh, Sarvesh is 5 years older than Gopal, and the sum of their ages is 61. What is Sakshi's age?
Let Gopal = 15 Then Sarvesh = 15 + 5 = 20 And Sakshi = 20 + 6 = 26 Check sum: 26 + 20 + 15 = 61 ✓
Question 16
If Pranay were 7 years younger, she would be 2/7 of Hailey's age 8 years from now. If Pranay is 37 years younger than Hailey, find Pranay's present age.
Thomas and Lily are twins. If Thomas is 30 years old now, how old was Lily 5 years ago?
Twins have the same age. 5 years ago, both were 30 - 5 = 25
Question 18
The difference between Camila and Kritika's ages is 20 years. In 5 years, Camila's age will be 2 times Kritika's age. How old is Camila now?
Let Kritika = x = 15 Then Camila = x + 20 = 15 + 20 = 35 Check: In 5 years, Camila+5 = 40 2 × (Kritika+5) = 2 × 20 = 40 ✓
Question 19
Calvin is 26 years old and Chetan is 13 years old. What will be their combined age after 5 years?
Calvin will be 26 + 5 = 31 Chetan will be 13 + 5 = 18 Combined = 31 + 18 = 49
Question 20
Four people: Kailash, Dhara, Preeti, Aurora
Given:
1. The sum of all four ages is 120
2. Kailash + Dhara = 50
3. Aurora is 8 years older than Preeti
4. Dhara is 28 years old
Find Preeti's age.
Step 1: From clue 4, Dhara = 28
Step 2: Using clue 2, we can find the other person in that pair
Step 3: Using clue 3 and clue 1, we can determine all ages