Intensive progress check 🎯 drill: 20 expert-level age-based puzzles questions. Worksheet 30 of 30 hones your difference ages abilities. Practice age puzzles, relative ages, age constraints under timed conditions. Best for expert-level students seeking challenging problems and time-bound practice.
Currently, Nilesh is 1/2 of Kenji's age. After 10 years, Nilesh will be 2/3 of Kenji's age. Find Nilesh's present age.
Let Kenji = x, then Nilesh = 1/2x After 10 years: 1/2x + 10 = 2/3(x + 10) Solving gives x = 40, so Nilesh = 20
Question 2
The average age of a family of 4 members (Clara, Vivek, Nicholas, Sudhir) is 31.5 years. If Sudhir (age 33) leaves the family, what will be the new average age?
Total age = 31.5 × 4 = 126 After Sudhir leaves: 126 - 33 = 93 New average = 93 ÷ 3 = 31
Question 3
Julian is 29 years old and Lillian is 14 years old. What will be the sum of their ages after 6 years?
Current sum = 29 + 14 = 43 After 6 years, each ages by 6, so sum increases by 12 Future sum = 43 + 12 = 55
Question 4
Lucas is 20 years old and Rakhi is 32 years old. What will be their combined age after 5 years?
Lucas will be 20 + 5 = 25 Rakhi will be 32 + 5 = 37 Combined = 25 + 37 = 62
Question 5
The average age of a family of 4 members (Ashish, Shailesh, Kinsley, Arjun) is 46.2 years. If Shailesh (age 44) leaves the family, what will be the new average age?
Total age = 46.2 × 4 = 185 After Shailesh leaves: 185 - 44 = 141 New average = 141 ÷ 3 = 47
Question 6
In a family of four: Vikram, Sahil, Gabriel, Divya. The eldest is 28, youngest is 5. The average age is 18. What is the sum of the ages of the other two members?
Total sum = 18 × 4 = 72 Eldest + youngest = 28 + 5 = 33 Sum of other two = 72 - 33 = 39
Question 7
Tournament participants: Allison, Sarika, Rahul, Dinesh
Given the following clues:
1. Allison is younger than Sarika
2. Sarika is younger than Rahul
3. Rahul is younger than Dinesh
4. Each person is exactly 3 years older than the person immediately younger than them.
5. Sarika is 22 years old.
Determine Rahul's age.
Step 1: From clues 1-3, the age order from youngest to oldest is: Allison → Sarika → Rahul → Dinesh
Step 2: From clue 4, each consecutive person differs by exactly 3 years. So if youngest = x, then: Allison=x, Sarika=x+3, Rahul=x+6, Dinesh=x+9
Step 3: From clue 5, Sarika (the 2nd) = 22 Therefore, x + 3 = 22 Solving: x = 22 - 3 = 19
The average age of a family of 6 members (Ezra, Navin, Veena, Deepti, Darpan, Vani) is 37.7 years. If Vani (age 21) leaves the family, what will be the new average age?
Total age = 37.7 × 6 = 226 After Vani leaves: 226 - 21 = 205 New average = 205 ÷ 5 = 41
Question 9
In a family, Farhan : Omar = 8:3 and Omar : Sheetal = 3:1. The sum of their ages is 36. Find Omar's age.
Let common ratio for Omar be 3 Then Farhan:Omar:Sheetal = 8:3:1 Sum of ratios = 12 Each unit = 36 ÷ 12 = 3 Omar's age = 3 × 3 = 9
Question 10
Hans is half as old as Nira was when Hans was 11 years old. If Nira is now 30 years old, find Hans's current age.
When Hans was 11 years old, that was 10 years ago At that time, Nira was 30 - 10 = 20 years old Now Hans is half of 20 Therefore, Hans's current age = 20 ÷ 2 = 10
Question 11
The product of the ages of Gopal and Everett is 156, and the sum of their ages is 25. Find Gopal's age.
Let ages be x and y. xy = 156 x + y = 25 Solving gives x = 12, y = 13 Therefore, Gopal's age = 13
Question 12
Andrew is 41 years old in 2024. In what year was Andrew born?
2024 - 41 = 1983
Question 13
Monika is 20 years old and Indira is 19 years old. What will be their combined age after 11 years?
Monika will be 20 + 11 = 31 Indira will be 19 + 11 = 30 Combined = 31 + 30 = 61
Question 14
Pallavi is 44 years older than Mike and is now 62 years old. How old was Pallavi 12 years ago?
Current age of Pallavi = 62 12 years ago = 62 - 12 = 50
Question 15
The product of the ages of Raul and Kenji is 400, and the sum of their ages is 41. Find Raul's age.
Let ages be x and y. xy = 400 x + y = 41 Solving gives x = 16, y = 25 Therefore, Raul's age = 25
Question 16
Omar is 1/2 of Heidi's age. After 6 years, Omar will be 2/3 of Heidi's age. Find Omar's present age.
Let Heidi = x, then Omar = 1/2x After 6 years: 1/2x + 6 = 2/3(x + 6) Solving gives x = 24, so Omar = 12
Question 17
When Brooklyn was born, Ajay was 12 years old. The sum of their present ages is 44. Find Brooklyn's age when Brooklyn was half of Ajay's age (this will happen 4 years ago).
Let Brooklyn's current age = 16, Ajay's current age = 28 Given: When Brooklyn was born (0 years old), Ajay was 12 years old. Therefore, Ajay is always 12 years older than Brooklyn. So 28 = 16 + 12 ✓
Condition: Find t such that Brooklyn's age = ½ of Ajay's age Equation: 16 + t = ½(28 + t) Multiply both sides by 2: 216 + 2t = 28 + t Simplify: 216 + 2t - t = 28 216 + t = 28 t = 28 - 216 t = 28 - 32 = -4
At that time, Brooklyn's age = 16 + -4 = 12 Verification: When Brooklyn is 12, Ajay is 24 = 24 Check: Is 12 = ½ × 24? ½ × 24 = 12.0 ✓
Note: Mathematically, this always equals the age difference (12) because: event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff
Question 18
If Dilip were 6 years younger, she would be 2/7 of Rajat's age 7 years from now. If Dilip is 32 years younger than Rajat, find Dilip's present age.
Let Rajat = 56, then Dilip = 24 Check: (24 - 6) = 2/7 × (56 + 7) 18 = 2/7 × 63 ✓
Question 19
In a family, Lily is the parent of Emma, and Max is the grandparent.
Lily is 2 times as old as Emma, and Max is 30 years older than Lily.
What is the age of Lily?
Let Emma (child) = 10 Then Lily (parent) = 2 × 10 = 20 Then Max (grandparent) = 20 + 30 = 50
Question 20
Ruby is 3 times as old as his son Tyler. After 4 years, the sum of their ages will be 40. How old is Tyler now?
Let son's age = x, then father's age = 3x After 4 years: (3x+4) + (x+4) = 40 (3+1)x + 8 = 40 (4)x = 32 x = 8
🏆 Congratulations on reaching the final worksheet! You've mastered Age-Based Puzzles!