Age at Event | Worksheet 8/10 - Advanced exam hall simulation

Question 1

When Elena was born, Seema was 5 years old. The sum of their present ages is 39. Find Elena's age when Elena was half of Seema's age (this will happen 12 years ago).

Let Elena's current age = 17, Seema's current age = 22
Given: When Elena was born (0 years old), Seema was 5 years old.
Therefore, Seema is always 5 years older than Elena.
So 22 = 17 + 5 ✓

Condition: Find t such that Elena's age = ½ of Seema's age
Equation: 17 + t = ½(22 + t)
Multiply both sides by 2: 217 + 2t = 22 + t
Simplify: 217 + 2t - t = 22
217 + t = 22
t = 22 - 217
t = 22 - 34 = -12

At that time, Elena's age = 17 + -12 = 5
Verification: When Elena is 5, Seema 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 2

When Jyoti was born, Ishaan was 18 years old. The sum of their present ages is 42. Find Jyoti's age when Jyoti was half of Ishaan's age (this will happen in 6 years).

Let Jyoti's current age = 12, Ishaan's current age = 30
Given: When Jyoti was born (0 years old), Ishaan was 18 years old.
Therefore, Ishaan is always 18 years older than Jyoti.
So 30 = 12 + 18 ✓

Condition: Find t such that Jyoti's age = ½ of Ishaan's age
Equation: 12 + t = ½(30 + t)
Multiply both sides by 2: 212 + 2t = 30 + t
Simplify: 212 + 2t - t = 30
212 + t = 30
t = 30 - 212
t = 30 - 24 = 6

At that time, Jyoti's age = 12 + 6 = 18
Verification: When Jyoti is 18, Ishaan 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

When Lucas was born, Prateek was 17 years old. The sum of their present ages is 79. Find Lucas's age when Lucas was half of Prateek's age (this will happen 14 years ago).

Let Lucas's current age = 31, Prateek's current age = 48
Given: When Lucas was born (0 years old), Prateek was 17 years old.
Therefore, Prateek is always 17 years older than Lucas.
So 48 = 31 + 17 ✓

Condition: Find t such that Lucas's age = ½ of Prateek's age
Equation: 31 + t = ½(48 + t)
Multiply both sides by 2: 231 + 2t = 48 + t
Simplify: 231 + 2t - t = 48
231 + t = 48
t = 48 - 231
t = 48 - 62 = -14

At that time, Lucas's age = 31 + -14 = 17
Verification: When Lucas is 17, Prateek is 34 = 34
Check: Is 17 = ½ × 34? ½ × 34 = 17.0 ✓

Note: Mathematically, this always equals the age difference (17) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 4

When Nira was born, Bhaskar was 6 years old. The sum of their present ages is 40. Find Nira's age when Nira was half of Bhaskar's age (this will happen 11 years ago).

Let Nira's current age = 17, Bhaskar's current age = 23
Given: When Nira was born (0 years old), Bhaskar was 6 years old.
Therefore, Bhaskar is always 6 years older than Nira.
So 23 = 17 + 6 ✓

Condition: Find t such that Nira's age = ½ of Bhaskar's age
Equation: 17 + t = ½(23 + t)
Multiply both sides by 2: 217 + 2t = 23 + t
Simplify: 217 + 2t - t = 23
217 + t = 23
t = 23 - 217
t = 23 - 34 = -11

At that time, Nira's age = 17 + -11 = 6
Verification: When Nira is 6, Bhaskar is 12 = 12
Check: Is 6 = ½ × 12? ½ × 12 = 6.0 ✓

Note: Mathematically, this always equals the age difference (6) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 5

When Wyatt was born, Colton was 22 years old. The sum of their present ages is 38. Find Wyatt's age when Wyatt was half of Colton's age (this will happen in 14 years).

Let Wyatt's current age = 8, Colton's current age = 30
Given: When Wyatt was born (0 years old), Colton was 22 years old.
Therefore, Colton is always 22 years older than Wyatt.
So 30 = 8 + 22 ✓

Condition: Find t such that Wyatt's age = ½ of Colton's age
Equation: 8 + t = ½(30 + t)
Multiply both sides by 2: 28 + 2t = 30 + t
Simplify: 28 + 2t - t = 30
28 + t = 30
t = 30 - 28
t = 30 - 16 = 14

At that time, Wyatt's age = 8 + 14 = 22
Verification: When Wyatt is 22, Colton is 44 = 44
Check: Is 22 = ½ × 44? ½ × 44 = 22.0 ✓

Note: Mathematically, this always equals the age difference (22) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 6

When Katia was born, Purvi was 12 years old. The sum of their present ages is 28. Find Katia's age when Katia was half of Purvi's age (this will happen in 4 years).

Let Katia's current age = 8, Purvi's current age = 20
Given: When Katia was born (0 years old), Purvi was 12 years old.
Therefore, Purvi is always 12 years older than Katia.
So 20 = 8 + 12 ✓

Condition: Find t such that Katia's age = ½ of Purvi's age
Equation: 8 + t = ½(20 + t)
Multiply both sides by 2: 28 + 2t = 20 + t
Simplify: 28 + 2t - t = 20
28 + t = 20
t = 20 - 28
t = 20 - 16 = 4

At that time, Katia's age = 8 + 4 = 12
Verification: When Katia is 12, Purvi 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 7

When Sarabjit was born, Sonam was 25 years old. The sum of their present ages is 51. Find Sarabjit's age when Sarabjit was half of Sonam's age (this will happen in 12 years).

Let Sarabjit's current age = 13, Sonam's current age = 38
Given: When Sarabjit was born (0 years old), Sonam was 25 years old.
Therefore, Sonam is always 25 years older than Sarabjit.
So 38 = 13 + 25 ✓

Condition: Find t such that Sarabjit's age = ½ of Sonam's age
Equation: 13 + t = ½(38 + t)
Multiply both sides by 2: 213 + 2t = 38 + t
Simplify: 213 + 2t - t = 38
213 + t = 38
t = 38 - 213
t = 38 - 26 = 12

At that time, Sarabjit's age = 13 + 12 = 25
Verification: When Sarabjit is 25, Sonam is 50 = 50
Check: Is 25 = ½ × 50? ½ × 50 = 25.0 ✓

Note: Mathematically, this always equals the age difference (25) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 8

When Mitali was born, Tanya was 7 years old. The sum of their present ages is 27. Find Mitali's age when Mitali was half of Tanya's age (this will happen 3 years ago).

Let Mitali's current age = 10, Tanya's current age = 17
Given: When Mitali was born (0 years old), Tanya was 7 years old.
Therefore, Tanya is always 7 years older than Mitali.
So 17 = 10 + 7 ✓

Condition: Find t such that Mitali's age = ½ of Tanya's age
Equation: 10 + t = ½(17 + t)
Multiply both sides by 2: 210 + 2t = 17 + t
Simplify: 210 + 2t - t = 17
210 + t = 17
t = 17 - 210
t = 17 - 20 = -3

At that time, Mitali's age = 10 + -3 = 7
Verification: When Mitali is 7, Tanya is 14 = 14
Check: Is 7 = ½ × 14? ½ × 14 = 7.0 ✓

Note: Mathematically, this always equals the age difference (7) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 9

When Bhaskar was born, Sunil was 6 years old. The sum of their present ages is 28. Find Bhaskar's age when Bhaskar was half of Sunil's age (this will happen 5 years ago).

Let Bhaskar's current age = 11, Sunil's current age = 17
Given: When Bhaskar was born (0 years old), Sunil was 6 years old.
Therefore, Sunil is always 6 years older than Bhaskar.
So 17 = 11 + 6 ✓

Condition: Find t such that Bhaskar's age = ½ of Sunil's age
Equation: 11 + t = ½(17 + t)
Multiply both sides by 2: 211 + 2t = 17 + t
Simplify: 211 + 2t - t = 17
211 + t = 17
t = 17 - 211
t = 17 - 22 = -5

At that time, Bhaskar's age = 11 + -5 = 6
Verification: When Bhaskar is 6, Sunil is 12 = 12
Check: Is 6 = ½ × 12? ½ × 12 = 6.0 ✓

Note: Mathematically, this always equals the age difference (6) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 10

When Sienna was born, Kunal was 17 years old. The sum of their present ages is 55. Find Sienna's age when Sienna was half of Kunal's age (this will happen 2 years ago).

Let Sienna's current age = 19, Kunal's current age = 36
Given: When Sienna was born (0 years old), Kunal was 17 years old.
Therefore, Kunal is always 17 years older than Sienna.
So 36 = 19 + 17 ✓

Condition: Find t such that Sienna's age = ½ of Kunal's age
Equation: 19 + t = ½(36 + t)
Multiply both sides by 2: 219 + 2t = 36 + t
Simplify: 219 + 2t - t = 36
219 + t = 36
t = 36 - 219
t = 36 - 38 = -2

At that time, Sienna's age = 19 + -2 = 17
Verification: When Sienna is 17, Kunal is 34 = 34
Check: Is 17 = ½ × 34? ½ × 34 = 17.0 ✓

Note: Mathematically, this always equals the age difference (17) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 11

When Shree was born, Christopher was 10 years old. The sum of their present ages is 20. Find Shree's age when Shree was half of Christopher's age (this will happen in 5 years).

Let Shree's current age = 5, Christopher's current age = 15
Given: When Shree was born (0 years old), Christopher was 10 years old.
Therefore, Christopher is always 10 years older than Shree.
So 15 = 5 + 10 ✓

Condition: Find t such that Shree's age = ½ of Christopher's age
Equation: 5 + t = ½(15 + t)
Multiply both sides by 2: 25 + 2t = 15 + t
Simplify: 25 + 2t - t = 15
25 + t = 15
t = 15 - 25
t = 15 - 10 = 5

At that time, Shree's age = 5 + 5 = 10
Verification: When Shree is 10, Christopher is 20 = 20
Check: Is 10 = ½ × 20? ½ × 20 = 10.0 ✓

Note: Mathematically, this always equals the age difference (10) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 12

When Anthony was born, Ganesh was 3 years old. The sum of their present ages is 13. Find Anthony's age when Anthony was half of Ganesh's age (this will happen 2 years ago).

Let Anthony's current age = 5, Ganesh's current age = 8
Given: When Anthony was born (0 years old), Ganesh was 3 years old.
Therefore, Ganesh is always 3 years older than Anthony.
So 8 = 5 + 3 ✓

Condition: Find t such that Anthony's age = ½ of Ganesh's age
Equation: 5 + t = ½(8 + t)
Multiply both sides by 2: 25 + 2t = 8 + t
Simplify: 25 + 2t - t = 8
25 + t = 8
t = 8 - 25
t = 8 - 10 = -2

At that time, Anthony's age = 5 + -2 = 3
Verification: When Anthony is 3, Ganesh is 6 = 6
Check: Is 3 = ½ × 6? ½ × 6 = 3.0 ✓

Note: Mathematically, this always equals the age difference (3) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 13

When Madelyn was born, Sanjay was 22 years old. The sum of their present ages is 54. Find Madelyn's age when Madelyn was half of Sanjay's age (this will happen in 6 years).

Let Madelyn's current age = 16, Sanjay's current age = 38
Given: When Madelyn was born (0 years old), Sanjay was 22 years old.
Therefore, Sanjay is always 22 years older than Madelyn.
So 38 = 16 + 22 ✓

Condition: Find t such that Madelyn's age = ½ of Sanjay's age
Equation: 16 + t = ½(38 + t)
Multiply both sides by 2: 216 + 2t = 38 + t
Simplify: 216 + 2t - t = 38
216 + t = 38
t = 38 - 216
t = 38 - 32 = 6

At that time, Madelyn's age = 16 + 6 = 22
Verification: When Madelyn is 22, Sanjay is 44 = 44
Check: Is 22 = ½ × 44? ½ × 44 = 22.0 ✓

Note: Mathematically, this always equals the age difference (22) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 14

When Ritika was born, Brooklyn was 19 years old. The sum of their present ages is 53. Find Ritika's age when Ritika was half of Brooklyn's age (this will happen in 2 years).

Let Ritika's current age = 17, Brooklyn's current age = 36
Given: When Ritika was born (0 years old), Brooklyn was 19 years old.
Therefore, Brooklyn is always 19 years older than Ritika.
So 36 = 17 + 19 ✓

Condition: Find t such that Ritika's age = ½ of Brooklyn's age
Equation: 17 + t = ½(36 + t)
Multiply both sides by 2: 217 + 2t = 36 + t
Simplify: 217 + 2t - t = 36
217 + t = 36
t = 36 - 217
t = 36 - 34 = 2

At that time, Ritika's age = 17 + 2 = 19
Verification: When Ritika is 19, Brooklyn is 38 = 38
Check: Is 19 = ½ × 38? ½ × 38 = 19.0 ✓

Note: Mathematically, this always equals the age difference (19) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 15

When Amrita was born, Durga was 21 years old. The sum of their present ages is 51. Find Amrita's age when Amrita was half of Durga's age (this will happen in 6 years).

Let Amrita's current age = 15, Durga's current age = 36
Given: When Amrita was born (0 years old), Durga was 21 years old.
Therefore, Durga is always 21 years older than Amrita.
So 36 = 15 + 21 ✓

Condition: Find t such that Amrita's age = ½ of Durga's age
Equation: 15 + t = ½(36 + t)
Multiply both sides by 2: 215 + 2t = 36 + t
Simplify: 215 + 2t - t = 36
215 + t = 36
t = 36 - 215
t = 36 - 30 = 6

At that time, Amrita's age = 15 + 6 = 21
Verification: When Amrita is 21, Durga 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 16

When Kritika was born, Charles was 15 years old. The sum of their present ages is 51. Find Kritika's age when Kritika was half of Charles's age (this will happen 3 years ago).

Let Kritika's current age = 18, Charles's current age = 33
Given: When Kritika was born (0 years old), Charles was 15 years old.
Therefore, Charles is always 15 years older than Kritika.
So 33 = 18 + 15 ✓

Condition: Find t such that Kritika's age = ½ of Charles's age
Equation: 18 + t = ½(33 + t)
Multiply both sides by 2: 218 + 2t = 33 + t
Simplify: 218 + 2t - t = 33
218 + t = 33
t = 33 - 218
t = 33 - 36 = -3

At that time, Kritika's age = 18 + -3 = 15
Verification: When Kritika is 15, Charles is 30 = 30
Check: Is 15 = ½ × 30? ½ × 30 = 15.0 ✓

Note: Mathematically, this always equals the age difference (15) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 17

When Madhav was born, Christopher was 15 years old. The sum of their present ages is 69. Find Madhav's age when Madhav was half of Christopher's age (this will happen 12 years ago).

Let Madhav's current age = 27, Christopher's current age = 42
Given: When Madhav was born (0 years old), Christopher was 15 years old.
Therefore, Christopher is always 15 years older than Madhav.
So 42 = 27 + 15 ✓

Condition: Find t such that Madhav's age = ½ of Christopher's age
Equation: 27 + t = ½(42 + t)
Multiply both sides by 2: 227 + 2t = 42 + t
Simplify: 227 + 2t - t = 42
227 + t = 42
t = 42 - 227
t = 42 - 54 = -12

At that time, Madhav's age = 27 + -12 = 15
Verification: When Madhav is 15, Christopher is 30 = 30
Check: Is 15 = ½ × 30? ½ × 30 = 15.0 ✓

Note: Mathematically, this always equals the age difference (15) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 18

When Finn was born, Nova was 22 years old. The sum of their present ages is 62. Find Finn's age when Finn was half of Nova's age (this will happen in 2 years).

Let Finn's current age = 20, Nova's current age = 42
Given: When Finn was born (0 years old), Nova was 22 years old.
Therefore, Nova is always 22 years older than Finn.
So 42 = 20 + 22 ✓

Condition: Find t such that Finn's age = ½ of Nova's age
Equation: 20 + t = ½(42 + t)
Multiply both sides by 2: 220 + 2t = 42 + t
Simplify: 220 + 2t - t = 42
220 + t = 42
t = 42 - 220
t = 42 - 40 = 2

At that time, Finn's age = 20 + 2 = 22
Verification: When Finn is 22, Nova is 44 = 44
Check: Is 22 = ½ × 44? ½ × 44 = 22.0 ✓

Note: Mathematically, this always equals the age difference (22) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 19

When Charlotte was born, Kenji was 22 years old. The sum of their present ages is 82. Find Charlotte's age when Charlotte was half of Kenji's age (this will happen 8 years ago).

Let Charlotte's current age = 30, Kenji's current age = 52
Given: When Charlotte was born (0 years old), Kenji was 22 years old.
Therefore, Kenji is always 22 years older than Charlotte.
So 52 = 30 + 22 ✓

Condition: Find t such that Charlotte's age = ½ of Kenji's age
Equation: 30 + t = ½(52 + t)
Multiply both sides by 2: 230 + 2t = 52 + t
Simplify: 230 + 2t - t = 52
230 + t = 52
t = 52 - 230
t = 52 - 60 = -8

At that time, Charlotte's age = 30 + -8 = 22
Verification: When Charlotte is 22, Kenji is 44 = 44
Check: Is 22 = ½ × 44? ½ × 44 = 22.0 ✓

Note: Mathematically, this always equals the age difference (22) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 20

When Shiva was born, Bella was 25 years old. The sum of their present ages is 67. Find Shiva's age when Shiva was half of Bella's age (this will happen in 4 years).

Let Shiva's current age = 21, Bella's current age = 46
Given: When Shiva was born (0 years old), Bella was 25 years old.
Therefore, Bella is always 25 years older than Shiva.
So 46 = 21 + 25 ✓

Condition: Find t such that Shiva's age = ½ of Bella's age
Equation: 21 + t = ½(46 + t)
Multiply both sides by 2: 221 + 2t = 46 + t
Simplify: 221 + 2t - t = 46
221 + t = 46
t = 46 - 221
t = 46 - 42 = 4

At that time, Shiva's age = 21 + 4 = 25
Verification: When Shiva is 25, Bella is 50 = 50
Check: Is 25 = ½ × 50? ½ × 50 = 25.0 ✓

Note: Mathematically, this always equals the age difference (25) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Age at Event Advanced Worksheet: Focus on exam-oriented approach Age at Event ADVANCED

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