Strategic basic drills ★ for age-based puzzles: 20 expert-level problems. Worksheet 29 of 30 - Focus: sum ages. Develop expertise in age comparison, age puzzles, relative ages with step-by-step solutions. Ideal for expert-level learners targeting challenging problems and time-bound practice.
Anu is 2 times as old as Nidhi. 4 years ago, the sum of their ages was 49. How old is Nidhi now?
Let Nidhi = x, then Anu = 2x 4 years ago: (2x - 4) + (x - 4) = 49 (2+1)x - 8 = 49 (3)x = 57 x = 19
Question 2
Aditya is half as old as Olivia was when Aditya was 21 years old. If Olivia is now 50 years old, find Aditya's current age.
When Aditya was 21 years old, that was 14 years ago At that time, Olivia was 50 - 14 = 36 years old Now Aditya is half of 36 Therefore, Aditya's current age = 36 ÷ 2 = 18
Question 3
11 years ago, the ratio of Jagdish's age to Shikha's age was 3:8. 22 years from now, the ratio will be 4:11. Find Jagdish's present age.
Let Jagdish's present age = x, Shikha's present age = y 11 years ago: (x-11)/(y-11) = 3/8 22 years from now: (x+22)/(y+22) = 4/11 Solving these equations gives x = 33, y = 88
Question 4
12 years ago, the ratio of Prerna's age to Arthur's age was 2:3. 24 years from now, the ratio will be 3:4. Find Prerna's present age.
Let Prerna's present age = x, Arthur's present age = y 12 years ago: (x-12)/(y-12) = 2/3 24 years from now: (x+24)/(y+24) = 3/4 Solving these equations gives x = 36, y = 54
Question 5
Isaac and Sebastian are twins. If Isaac is 13 years old now, how old was Sebastian 5 years ago?
Twins have the same age. 5 years ago, both were 13 - 5 = 8
Question 6
Grace is 3 times as old as his son Vedika. After 8 years, the sum of their ages will be 48. How old is Vedika now?
Let son's age = x, then father's age = 3x After 8 years: (3x+8) + (x+8) = 48 (3+1)x + 16 = 48 (4)x = 32 x = 8
Question 7
When Ashwin was born, Naresh was 5 years old. The sum of their present ages is 27. Find Ashwin's age when Ashwin was half of Naresh's age (this will happen 6 years ago).
Let Ashwin's current age = 11, Naresh's current age = 16 Given: When Ashwin was born (0 years old), Naresh was 5 years old. Therefore, Naresh is always 5 years older than Ashwin. So 16 = 11 + 5 ✓
Condition: Find t such that Ashwin's age = ½ of Naresh's age Equation: 11 + t = ½(16 + t) Multiply both sides by 2: 211 + 2t = 16 + t Simplify: 211 + 2t - t = 16 211 + t = 16 t = 16 - 211 t = 16 - 22 = -6
At that time, Ashwin's age = 11 + -6 = 5 Verification: When Ashwin is 5, Naresh is 10 = 10 Check: Is 5 = ½ × 10? ½ × 10 = 5.0 ✓
Note: Mathematically, this always equals the age difference (5) because: event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff
Question 8
Tournament participants: Asha, Dhruv, Aryan, Aparna
Given the following clues:
1. Asha is younger than Dhruv
2. Dhruv is younger than Aryan
3. Aryan is younger than Aparna
4. Each person is exactly 5 years older than the person immediately younger than them.
5. Aryan is 25 years old.
Determine Dhruv's age.
Step 1: From clues 1-3, the age order from youngest to oldest is: Asha → Dhruv → Aryan → Aparna
Step 2: From clue 4, each consecutive person differs by exactly 5 years. So if youngest = x, then: Asha=x, Dhruv=x+5, Aryan=x+10, Aparna=x+15
Step 3: From clue 5, Aryan (the 3rd) = 25 Therefore, x + 10 = 25 Solving: x = 25 - 10 = 15
Suman is half as old as Andrew was when Suman was 26 years old. If Andrew is now 52 years old, find Suman's current age.
When Suman was 26 years old, that was 12 years ago At that time, Andrew was 52 - 12 = 40 years old Now Suman is half of 40 Therefore, Suman's current age = 40 ÷ 2 = 20
Question 10
Tournament participants: Ravi, Darpan, Aish, Mason
Given the following clues:
1. Ravi is younger than Darpan
2. Darpan is younger than Aish
3. Aish is younger than Mason
4. Each person is exactly 4 years older than the person immediately younger than them.
5. Ravi is 24 years old.
Determine Mason's age.
Step 1: From clues 1-3, the age order from youngest to oldest is: Ravi → Darpan → Aish → Mason
Step 2: From clue 4, each consecutive person differs by exactly 4 years. So if youngest = x, then: Ravi=x, Darpan=x+4, Aish=x+8, Mason=x+12
Step 3: From clue 5, Ravi (the 1st (youngest)) = 24 Therefore, x + 0 = 24 Solving: x = 24 - 0 = 24
Step 5: Mason is the 4th (oldest). Therefore, Mason = 36
Question 11
If Bela were 6 years younger, she would be 3/8 of Isabella's age 4 years from now. If Bela is 6 years younger than Isabella, find Bela's present age.
Let Isabella = 30, then Bela = 24 Check: (24 - 6) = 3/8 × (30 + 4) 18 = 3/8 × 34 ✓
Question 12
12 years ago, the ratio of Santosh's age to Emery's age was 2:3. 24 years from now, the ratio will be 3:4. Find Santosh's present age.
Let Santosh's present age = x, Emery's present age = y 12 years ago: (x-12)/(y-12) = 2/3 24 years from now: (x+24)/(y+24) = 3/4 Solving these equations gives x = 36, y = 54
Question 13
Zane is 20 years old in 2024. In what year was Zane born?
2024 - 20 = 2004
Question 14
The product of the ages of Upasana and Rakhi is 48, and the difference between their ages is 2. Find Upasana's age.
Let ages be x and y. xy = 48 x - y = 2 Solving gives x = 6, y = 8 Therefore, Upasana's age = 6
Question 15
Tournament participants: Bjorn, Miles, Aubrey, Kennedy
Given the following clues:
1. Bjorn is younger than Miles
2. Miles is younger than Aubrey
3. Aubrey is younger than Kennedy
4. Each person is exactly 4 years older than the person immediately younger than them.
5. Aubrey is 29 years old.
Determine Kennedy's age.
Step 1: From clues 1-3, the age order from youngest to oldest is: Bjorn → Miles → Aubrey → Kennedy
Step 2: From clue 4, each consecutive person differs by exactly 4 years. So if youngest = x, then: Bjorn=x, Miles=x+4, Aubrey=x+8, Kennedy=x+12
Step 3: From clue 5, Aubrey (the 3rd) = 29 Therefore, x + 8 = 29 Solving: x = 29 - 8 = 21
Step 5: Kennedy is the 4th (oldest). Therefore, Kennedy = 33
Question 16
The product of the ages of Genesis, Beau, and Nira is 384. The eldest is 3 times the youngest, and the middle child's age is between them. Find the age of the eldest.
Let youngest = x, then eldest = 3x Then middle = 384 ÷ (x × 3x) = 384 ÷ (3x²) Testing x = 4: middle = 384 ÷ (3 × 4²) = 8 Therefore, eldest = 12
Question 17
If Noah were 4 years younger, she would be 2/3 of Madhu's age 5 years from now. If Noah is 9 years younger than Madhu, find Noah's present age.
Rajat is 3 times as old as Elias. 6 years ago, the sum of their ages was 52. How old is Elias now?
Let Elias = x, then Rajat = 3x 6 years ago: (3x - 6) + (x - 6) = 52 (3+1)x - 12 = 52 (4)x = 64 x = 16
Question 19
The product of the ages of Meena and Alok is 360, and the sum of their ages is 38. Find Meena's age.
Let ages be x and y. xy = 360 x + y = 38 Solving gives x = 18, y = 20 Therefore, Meena's age = 20
Question 20
If Narendra were 8 years younger, she would be 2/5 of Rashmi's age 9 years from now. If Narendra is 32 years younger than Rashmi, find Narendra's present age.