Age at Event | Worksheet 9/10 - Expert skill evaluation ⚡

Question 1

When Calvin was born, Shivam was 11 years old. The sum of their present ages is 45. Find Calvin's age when Calvin was half of Shivam's age (this will happen 6 years ago).

Let Calvin's current age = 17, Shivam's current age = 28
Given: When Calvin was born (0 years old), Shivam was 11 years old.
Therefore, Shivam is always 11 years older than Calvin.
So 28 = 17 + 11 ✓

Condition: Find t such that Calvin's age = ½ of Shivam's age
Equation: 17 + t = ½(28 + t)
Multiply both sides by 2: 217 + 2t = 28 + t
Simplify: 217 + 2t - t = 28
217 + t = 28
t = 28 - 217
t = 28 - 34 = -6

At that time, Calvin's age = 17 + -6 = 11
Verification: When Calvin is 11, Shivam is 22 = 22
Check: Is 11 = ½ × 22? ½ × 22 = 11.0 ✓

Note: Mathematically, this always equals the age difference (11) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 2

When Lakshmi was born, Jackson was 19 years old. The sum of their present ages is 87. Find Lakshmi's age when Lakshmi was half of Jackson's age (this will happen 15 years ago).

Let Lakshmi's current age = 34, Jackson's current age = 53
Given: When Lakshmi was born (0 years old), Jackson was 19 years old.
Therefore, Jackson is always 19 years older than Lakshmi.
So 53 = 34 + 19 ✓

Condition: Find t such that Lakshmi's age = ½ of Jackson's age
Equation: 34 + t = ½(53 + t)
Multiply both sides by 2: 234 + 2t = 53 + t
Simplify: 234 + 2t - t = 53
234 + t = 53
t = 53 - 234
t = 53 - 68 = -15

At that time, Lakshmi's age = 34 + -15 = 19
Verification: When Lakshmi is 19, Jackson 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 3

When Violet was born, Samantha was 5 years old. The sum of their present ages is 45. Find Violet's age when Violet was half of Samantha's age (this will happen 15 years ago).

Let Violet's current age = 20, Samantha's current age = 25
Given: When Violet was born (0 years old), Samantha was 5 years old.
Therefore, Samantha is always 5 years older than Violet.
So 25 = 20 + 5 ✓

Condition: Find t such that Violet's age = ½ of Samantha's age
Equation: 20 + t = ½(25 + t)
Multiply both sides by 2: 220 + 2t = 25 + t
Simplify: 220 + 2t - t = 25
220 + t = 25
t = 25 - 220
t = 25 - 40 = -15

At that time, Violet's age = 20 + -15 = 5
Verification: When Violet is 5, Samantha 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 4

When Sunita was born, Shravan was 19 years old. The sum of their present ages is 59. Find Sunita's age when Sunita was half of Shravan's age (this will happen 1 years ago).

Let Sunita's current age = 20, Shravan's current age = 39
Given: When Sunita was born (0 years old), Shravan was 19 years old.
Therefore, Shravan is always 19 years older than Sunita.
So 39 = 20 + 19 ✓

Condition: Find t such that Sunita's age = ½ of Shravan's age
Equation: 20 + t = ½(39 + t)
Multiply both sides by 2: 220 + 2t = 39 + t
Simplify: 220 + 2t - t = 39
220 + t = 39
t = 39 - 220
t = 39 - 40 = -1

At that time, Sunita's age = 20 + -1 = 19
Verification: When Sunita is 19, Shravan 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 5

When Shilpa was born, Diego was 9 years old. The sum of their present ages is 35. Find Shilpa's age when Shilpa was half of Diego's age (this will happen 4 years ago).

Let Shilpa's current age = 13, Diego's current age = 22
Given: When Shilpa was born (0 years old), Diego was 9 years old.
Therefore, Diego is always 9 years older than Shilpa.
So 22 = 13 + 9 ✓

Condition: Find t such that Shilpa's age = ½ of Diego's age
Equation: 13 + t = ½(22 + t)
Multiply both sides by 2: 213 + 2t = 22 + t
Simplify: 213 + 2t - t = 22
213 + t = 22
t = 22 - 213
t = 22 - 26 = -4

At that time, Shilpa's age = 13 + -4 = 9
Verification: When Shilpa is 9, Diego is 18 = 18
Check: Is 9 = ½ × 18? ½ × 18 = 9.0 ✓

Note: Mathematically, this always equals the age difference (9) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 6

When Vishal was born, Austin was 9 years old. The sum of their present ages is 53. Find Vishal's age when Vishal was half of Austin's age (this will happen 13 years ago).

Let Vishal's current age = 22, Austin's current age = 31
Given: When Vishal was born (0 years old), Austin was 9 years old.
Therefore, Austin is always 9 years older than Vishal.
So 31 = 22 + 9 ✓

Condition: Find t such that Vishal's age = ½ of Austin's age
Equation: 22 + t = ½(31 + t)
Multiply both sides by 2: 222 + 2t = 31 + t
Simplify: 222 + 2t - t = 31
222 + t = 31
t = 31 - 222
t = 31 - 44 = -13

At that time, Vishal's age = 22 + -13 = 9
Verification: When Vishal is 9, Austin is 18 = 18
Check: Is 9 = ½ × 18? ½ × 18 = 9.0 ✓

Note: Mathematically, this always equals the age difference (9) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 7

When Manjari was born, Mohan was 11 years old. The sum of their present ages is 53. Find Manjari's age when Manjari was half of Mohan's age (this will happen 10 years ago).

Let Manjari's current age = 21, Mohan's current age = 32
Given: When Manjari was born (0 years old), Mohan was 11 years old.
Therefore, Mohan is always 11 years older than Manjari.
So 32 = 21 + 11 ✓

Condition: Find t such that Manjari's age = ½ of Mohan's age
Equation: 21 + t = ½(32 + t)
Multiply both sides by 2: 221 + 2t = 32 + t
Simplify: 221 + 2t - t = 32
221 + t = 32
t = 32 - 221
t = 32 - 42 = -10

At that time, Manjari's age = 21 + -10 = 11
Verification: When Manjari is 11, Mohan is 22 = 22
Check: Is 11 = ½ × 22? ½ × 22 = 11.0 ✓

Note: Mathematically, this always equals the age difference (11) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 8

When Drishti was born, Uma was 12 years old. The sum of their present ages is 54. Find Drishti's age when Drishti was half of Uma's age (this will happen 9 years ago).

Let Drishti's current age = 21, Uma's current age = 33
Given: When Drishti was born (0 years old), Uma was 12 years old.
Therefore, Uma is always 12 years older than Drishti.
So 33 = 21 + 12 ✓

Condition: Find t such that Drishti's age = ½ of Uma's age
Equation: 21 + t = ½(33 + t)
Multiply both sides by 2: 221 + 2t = 33 + t
Simplify: 221 + 2t - t = 33
221 + t = 33
t = 33 - 221
t = 33 - 42 = -9

At that time, Drishti's age = 21 + -9 = 12
Verification: When Drishti is 12, Uma 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 9

When Dhara was born, Vedika was 20 years old. The sum of their present ages is 84. Find Dhara's age when Dhara was half of Vedika's age (this will happen 12 years ago).

Let Dhara's current age = 32, Vedika's current age = 52
Given: When Dhara was born (0 years old), Vedika was 20 years old.
Therefore, Vedika is always 20 years older than Dhara.
So 52 = 32 + 20 ✓

Condition: Find t such that Dhara's age = ½ of Vedika's age
Equation: 32 + t = ½(52 + t)
Multiply both sides by 2: 232 + 2t = 52 + t
Simplify: 232 + 2t - t = 52
232 + t = 52
t = 52 - 232
t = 52 - 64 = -12

At that time, Dhara's age = 32 + -12 = 20
Verification: When Dhara is 20, Vedika is 40 = 40
Check: Is 20 = ½ × 40? ½ × 40 = 20.0 ✓

Note: Mathematically, this always equals the age difference (20) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 10

When Seema was born, Hailey was 14 years old. The sum of their present ages is 68. Find Seema's age when Seema was half of Hailey's age (this will happen 13 years ago).

Let Seema's current age = 27, Hailey's current age = 41
Given: When Seema was born (0 years old), Hailey was 14 years old.
Therefore, Hailey is always 14 years older than Seema.
So 41 = 27 + 14 ✓

Condition: Find t such that Seema's age = ½ of Hailey's age
Equation: 27 + t = ½(41 + t)
Multiply both sides by 2: 227 + 2t = 41 + t
Simplify: 227 + 2t - t = 41
227 + t = 41
t = 41 - 227
t = 41 - 54 = -13

At that time, Seema's age = 27 + -13 = 14
Verification: When Seema is 14, Hailey is 28 = 28
Check: Is 14 = ½ × 28? ½ × 28 = 14.0 ✓

Note: Mathematically, this always equals the age difference (14) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 11

When Sunil was born, Utkarsh was 16 years old. The sum of their present ages is 36. Find Sunil's age when Sunil was half of Utkarsh's age (this will happen in 6 years).

Let Sunil's current age = 10, Utkarsh's current age = 26
Given: When Sunil was born (0 years old), Utkarsh was 16 years old.
Therefore, Utkarsh is always 16 years older than Sunil.
So 26 = 10 + 16 ✓

Condition: Find t such that Sunil's age = ½ of Utkarsh's age
Equation: 10 + t = ½(26 + t)
Multiply both sides by 2: 210 + 2t = 26 + t
Simplify: 210 + 2t - t = 26
210 + t = 26
t = 26 - 210
t = 26 - 20 = 6

At that time, Sunil's age = 10 + 6 = 16
Verification: When Sunil is 16, Utkarsh is 32 = 32
Check: Is 16 = ½ × 32? ½ × 32 = 16.0 ✓

Note: Mathematically, this always equals the age difference (16) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 12

When Sarika was born, Vivek was 20 years old. The sum of their present ages is 80. Find Sarika's age when Sarika was half of Vivek's age (this will happen 10 years ago).

Let Sarika's current age = 30, Vivek's current age = 50
Given: When Sarika was born (0 years old), Vivek was 20 years old.
Therefore, Vivek is always 20 years older than Sarika.
So 50 = 30 + 20 ✓

Condition: Find t such that Sarika's age = ½ of Vivek's age
Equation: 30 + t = ½(50 + t)
Multiply both sides by 2: 230 + 2t = 50 + t
Simplify: 230 + 2t - t = 50
230 + t = 50
t = 50 - 230
t = 50 - 60 = -10

At that time, Sarika's age = 30 + -10 = 20
Verification: When Sarika is 20, Vivek is 40 = 40
Check: Is 20 = ½ × 40? ½ × 40 = 20.0 ✓

Note: Mathematically, this always equals the age difference (20) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 13

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

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

Condition: Find t such that Freya's age = ½ of Ujjwal'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, Freya's age = 10 + -3 = 7
Verification: When Freya is 7, Ujjwal 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 14

When Tanu was born, Bennett was 5 years old. The sum of their present ages is 23. Find Tanu's age when Tanu was half of Bennett's age (this will happen 4 years ago).

Let Tanu's current age = 9, Bennett's current age = 14
Given: When Tanu was born (0 years old), Bennett was 5 years old.
Therefore, Bennett is always 5 years older than Tanu.
So 14 = 9 + 5 ✓

Condition: Find t such that Tanu's age = ½ of Bennett's age
Equation: 9 + t = ½(14 + t)
Multiply both sides by 2: 29 + 2t = 14 + t
Simplify: 29 + 2t - t = 14
29 + t = 14
t = 14 - 29
t = 14 - 18 = -4

At that time, Tanu's age = 9 + -4 = 5
Verification: When Tanu is 5, Bennett 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 15

When Dylan was born, Tanya was 15 years old. The sum of their present ages is 25. Find Dylan's age when Dylan was half of Tanya's age (this will happen in 10 years).

Let Dylan's current age = 5, Tanya's current age = 20
Given: When Dylan was born (0 years old), Tanya was 15 years old.
Therefore, Tanya is always 15 years older than Dylan.
So 20 = 5 + 15 ✓

Condition: Find t such that Dylan's age = ½ of Tanya's age
Equation: 5 + t = ½(20 + t)
Multiply both sides by 2: 25 + 2t = 20 + t
Simplify: 25 + 2t - t = 20
25 + t = 20
t = 20 - 25
t = 20 - 10 = 10

At that time, Dylan's age = 5 + 10 = 15
Verification: When Dylan is 15, Tanya 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 16

When Indu was born, Nidhi was 8 years old. The sum of their present ages is 42. Find Indu's age when Indu was half of Nidhi's age (this will happen 9 years ago).

Let Indu's current age = 17, Nidhi's current age = 25
Given: When Indu was born (0 years old), Nidhi was 8 years old.
Therefore, Nidhi is always 8 years older than Indu.
So 25 = 17 + 8 ✓

Condition: Find t such that Indu's age = ½ of Nidhi's age
Equation: 17 + t = ½(25 + t)
Multiply both sides by 2: 217 + 2t = 25 + t
Simplify: 217 + 2t - t = 25
217 + t = 25
t = 25 - 217
t = 25 - 34 = -9

At that time, Indu's age = 17 + -9 = 8
Verification: When Indu is 8, Nidhi is 16 = 16
Check: Is 8 = ½ × 16? ½ × 16 = 8.0 ✓

Note: Mathematically, this always equals the age difference (8) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 17

When Serenity was born, Hitesh was 22 years old. The sum of their present ages is 58. Find Serenity's age when Serenity was half of Hitesh's age (this will happen in 4 years).

Let Serenity's current age = 18, Hitesh's current age = 40
Given: When Serenity was born (0 years old), Hitesh was 22 years old.
Therefore, Hitesh is always 22 years older than Serenity.
So 40 = 18 + 22 ✓

Condition: Find t such that Serenity's age = ½ of Hitesh's age
Equation: 18 + t = ½(40 + t)
Multiply both sides by 2: 218 + 2t = 40 + t
Simplify: 218 + 2t - t = 40
218 + t = 40
t = 40 - 218
t = 40 - 36 = 4

At that time, Serenity's age = 18 + 4 = 22
Verification: When Serenity is 22, Hitesh 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 18

When Piya was born, Isla was 18 years old. The sum of their present ages is 64. Find Piya's age when Piya was half of Isla's age (this will happen 5 years ago).

Let Piya's current age = 23, Isla's current age = 41
Given: When Piya was born (0 years old), Isla was 18 years old.
Therefore, Isla is always 18 years older than Piya.
So 41 = 23 + 18 ✓

Condition: Find t such that Piya's age = ½ of Isla's age
Equation: 23 + t = ½(41 + t)
Multiply both sides by 2: 223 + 2t = 41 + t
Simplify: 223 + 2t - t = 41
223 + t = 41
t = 41 - 223
t = 41 - 46 = -5

At that time, Piya's age = 23 + -5 = 18
Verification: When Piya is 18, Isla 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 19

When Bryson was born, Shubh was 5 years old. The sum of their present ages is 37. Find Bryson's age when Bryson was half of Shubh's age (this will happen 11 years ago).

Let Bryson's current age = 16, Shubh's current age = 21
Given: When Bryson was born (0 years old), Shubh was 5 years old.
Therefore, Shubh is always 5 years older than Bryson.
So 21 = 16 + 5 ✓

Condition: Find t such that Bryson's age = ½ of Shubh's age
Equation: 16 + t = ½(21 + t)
Multiply both sides by 2: 216 + 2t = 21 + t
Simplify: 216 + 2t - t = 21
216 + t = 21
t = 21 - 216
t = 21 - 32 = -11

At that time, Bryson's age = 16 + -11 = 5
Verification: When Bryson is 5, Shubh 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 20

When Ezra was born, Jyoti was 6 years old. The sum of their present ages is 32. Find Ezra's age when Ezra was half of Jyoti's age (this will happen 7 years ago).

Let Ezra's current age = 13, Jyoti's current age = 19
Given: When Ezra was born (0 years old), Jyoti was 6 years old.
Therefore, Jyoti is always 6 years older than Ezra.
So 19 = 13 + 6 ✓

Condition: Find t such that Ezra's age = ½ of Jyoti's age
Equation: 13 + t = ½(19 + t)
Multiply both sides by 2: 213 + 2t = 19 + t
Simplify: 213 + 2t - t = 19
213 + t = 19
t = 19 - 213
t = 19 - 26 = -7

At that time, Ezra's age = 13 + -7 = 6
Verification: When Ezra is 6, Jyoti 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

Age at Event - Expert Level: conceptual clarity Age at Event EXPERT

What you'll learn in this worksheet: