Age at Event Beginner-Intermediate Worksheet: Focus on common variations practice Age at Event BEGINNER INTERMEDIATE

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

Condition: Find t such that Karthik's age = ½ of Satish's age
Equation: 5 + t = ½(21 + t)
Multiply both sides by 2: 25 + 2t = 21 + t
Simplify: 25 + 2t - t = 21
25 + t = 21
t = 21 - 25
t = 21 - 10 = 11

At that time, Karthik's age = 5 + 11 = 16
Verification: When Karthik is 16, Satish 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

Let Ankur's current age = 13, Alexander's current age = 16
Given: When Ankur was born (0 years old), Alexander was 3 years old.
Therefore, Alexander is always 3 years older than Ankur.
So 16 = 13 + 3 ✓

Condition: Find t such that Ankur's age = ½ of Alexander's age
Equation: 13 + t = ½(16 + t)
Multiply both sides by 2: 213 + 2t = 16 + t
Simplify: 213 + 2t - t = 16
213 + t = 16
t = 16 - 213
t = 16 - 26 = -10

At that time, Ankur's age = 13 + -10 = 3
Verification: When Ankur is 3, Alexander 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

Let Ella's current age = 28, Yogesh's current age = 43
Given: When Ella was born (0 years old), Yogesh was 15 years old.
Therefore, Yogesh is always 15 years older than Ella.
So 43 = 28 + 15 ✓

Condition: Find t such that Ella's age = ½ of Yogesh's age
Equation: 28 + t = ½(43 + t)
Multiply both sides by 2: 228 + 2t = 43 + t
Simplify: 228 + 2t - t = 43
228 + t = 43
t = 43 - 228
t = 43 - 56 = -13

At that time, Ella's age = 28 + -13 = 15
Verification: When Ella is 15, Yogesh 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

Let Manoj's current age = 22, David's current age = 34
Given: When Manoj was born (0 years old), David was 12 years old.
Therefore, David is always 12 years older than Manoj.
So 34 = 22 + 12 ✓

Condition: Find t such that Manoj's age = ½ of David's age
Equation: 22 + t = ½(34 + t)
Multiply both sides by 2: 222 + 2t = 34 + t
Simplify: 222 + 2t - t = 34
222 + t = 34
t = 34 - 222
t = 34 - 44 = -10

At that time, Manoj's age = 22 + -10 = 12
Verification: When Manoj is 12, David 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

Let Riya's current age = 5, Bharat's current age = 12
Given: When Riya was born (0 years old), Bharat was 7 years old.
Therefore, Bharat is always 7 years older than Riya.
So 12 = 5 + 7 ✓

Condition: Find t such that Riya's age = ½ of Bharat's age
Equation: 5 + t = ½(12 + t)
Multiply both sides by 2: 25 + 2t = 12 + t
Simplify: 25 + 2t - t = 12
25 + t = 12
t = 12 - 25
t = 12 - 10 = 2

At that time, Riya's age = 5 + 2 = 7
Verification: When Riya is 7, Bharat 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

Let Ellie's current age = 12, Vinay's current age = 22
Given: When Ellie was born (0 years old), Vinay was 10 years old.
Therefore, Vinay is always 10 years older than Ellie.
So 22 = 12 + 10 ✓

Condition: Find t such that Ellie's age = ½ of Vinay's age
Equation: 12 + t = ½(22 + t)
Multiply both sides by 2: 212 + 2t = 22 + t
Simplify: 212 + 2t - t = 22
212 + t = 22
t = 22 - 212
t = 22 - 24 = -2

At that time, Ellie's age = 12 + -2 = 10
Verification: When Ellie is 10, Vinay 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

Let Dominic's current age = 9, Sonal's current age = 28
Given: When Dominic was born (0 years old), Sonal was 19 years old.
Therefore, Sonal is always 19 years older than Dominic.
So 28 = 9 + 19 ✓

Condition: Find t such that Dominic's age = ½ of Sonal's age
Equation: 9 + t = ½(28 + t)
Multiply both sides by 2: 29 + 2t = 28 + t
Simplify: 29 + 2t - t = 28
29 + t = 28
t = 28 - 29
t = 28 - 18 = 10

At that time, Dominic's age = 9 + 10 = 19
Verification: When Dominic is 19, Sonal 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

Let Sarah's current age = 21, Muskan's current age = 40
Given: When Sarah was born (0 years old), Muskan was 19 years old.
Therefore, Muskan is always 19 years older than Sarah.
So 40 = 21 + 19 ✓

Condition: Find t such that Sarah's age = ½ of Muskan's age
Equation: 21 + t = ½(40 + t)
Multiply both sides by 2: 221 + 2t = 40 + t
Simplify: 221 + 2t - t = 40
221 + t = 40
t = 40 - 221
t = 40 - 42 = -2

At that time, Sarah's age = 21 + -2 = 19
Verification: When Sarah is 19, Muskan 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

Let Eliana's current age = 22, Kavita's current age = 43
Given: When Eliana was born (0 years old), Kavita was 21 years old.
Therefore, Kavita is always 21 years older than Eliana.
So 43 = 22 + 21 ✓

Condition: Find t such that Eliana's age = ½ of Kavita's age
Equation: 22 + t = ½(43 + t)
Multiply both sides by 2: 222 + 2t = 43 + t
Simplify: 222 + 2t - t = 43
222 + t = 43
t = 43 - 222
t = 43 - 44 = -1

At that time, Eliana's age = 22 + -1 = 21
Verification: When Eliana is 21, Kavita 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

Let Yamini's current age = 18, Anshul's current age = 42
Given: When Yamini was born (0 years old), Anshul was 24 years old.
Therefore, Anshul is always 24 years older than Yamini.
So 42 = 18 + 24 ✓

Condition: Find t such that Yamini's age = ½ of Anshul's age
Equation: 18 + t = ½(42 + t)
Multiply both sides by 2: 218 + 2t = 42 + t
Simplify: 218 + 2t - t = 42
218 + t = 42
t = 42 - 218
t = 42 - 36 = 6

At that time, Yamini's age = 18 + 6 = 24
Verification: When Yamini is 24, Anshul is 48 = 48
Check: Is 24 = ½ × 48? ½ × 48 = 24.0 ✓

Note: Mathematically, this always equals the age difference (24) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

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

Condition: Find t such that Rashmi's age = ½ of Hans's age
Equation: 25 + t = ½(38 + t)
Multiply both sides by 2: 225 + 2t = 38 + t
Simplify: 225 + 2t - t = 38
225 + t = 38
t = 38 - 225
t = 38 - 50 = -12

At that time, Rashmi's age = 25 + -12 = 13
Verification: When Rashmi is 13, Hans is 26 = 26
Check: Is 13 = ½ × 26? ½ × 26 = 13.0 ✓

Note: Mathematically, this always equals the age difference (13) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Let Lata's current age = 28, Laksh's current age = 53
Given: When Lata was born (0 years old), Laksh was 25 years old.
Therefore, Laksh is always 25 years older than Lata.
So 53 = 28 + 25 ✓

Condition: Find t such that Lata's age = ½ of Laksh's age
Equation: 28 + t = ½(53 + t)
Multiply both sides by 2: 228 + 2t = 53 + t
Simplify: 228 + 2t - t = 53
228 + t = 53
t = 53 - 228
t = 53 - 56 = -3

At that time, Lata's age = 28 + -3 = 25
Verification: When Lata is 25, Laksh 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

Let Dhruv's current age = 23, Saachi's current age = 48
Given: When Dhruv was born (0 years old), Saachi was 25 years old.
Therefore, Saachi is always 25 years older than Dhruv.
So 48 = 23 + 25 ✓

Condition: Find t such that Dhruv's age = ½ of Saachi's age
Equation: 23 + t = ½(48 + t)
Multiply both sides by 2: 223 + 2t = 48 + t
Simplify: 223 + 2t - t = 48
223 + t = 48
t = 48 - 223
t = 48 - 46 = 2

At that time, Dhruv's age = 23 + 2 = 25
Verification: When Dhruv is 25, Saachi 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

Let Ganesh's current age = 14, Adam's current age = 27
Given: When Ganesh was born (0 years old), Adam was 13 years old.
Therefore, Adam is always 13 years older than Ganesh.
So 27 = 14 + 13 ✓

Condition: Find t such that Ganesh's age = ½ of Adam's age
Equation: 14 + t = ½(27 + t)
Multiply both sides by 2: 214 + 2t = 27 + t
Simplify: 214 + 2t - t = 27
214 + t = 27
t = 27 - 214
t = 27 - 28 = -1

At that time, Ganesh's age = 14 + -1 = 13
Verification: When Ganesh is 13, Adam is 26 = 26
Check: Is 13 = ½ × 26? ½ × 26 = 13.0 ✓

Note: Mathematically, this always equals the age difference (13) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Let Shalini's current age = 6, Ashwin's current age = 16
Given: When Shalini was born (0 years old), Ashwin was 10 years old.
Therefore, Ashwin is always 10 years older than Shalini.
So 16 = 6 + 10 ✓

Condition: Find t such that Shalini's age = ½ of Ashwin's age
Equation: 6 + t = ½(16 + t)
Multiply both sides by 2: 26 + 2t = 16 + t
Simplify: 26 + 2t - t = 16
26 + t = 16
t = 16 - 26
t = 16 - 12 = 4

At that time, Shalini's age = 6 + 4 = 10
Verification: When Shalini is 10, Ashwin 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

Let Utkarsh's current age = 11, Louis's current age = 16
Given: When Utkarsh was born (0 years old), Louis was 5 years old.
Therefore, Louis is always 5 years older than Utkarsh.
So 16 = 11 + 5 ✓

Condition: Find t such that Utkarsh's age = ½ of Louis'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, Utkarsh's age = 11 + -6 = 5
Verification: When Utkarsh is 5, Louis 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

Let Ella's current age = 7, Kinsley's current age = 12
Given: When Ella was born (0 years old), Kinsley was 5 years old.
Therefore, Kinsley is always 5 years older than Ella.
So 12 = 7 + 5 ✓

Condition: Find t such that Ella's age = ½ of Kinsley's age
Equation: 7 + t = ½(12 + t)
Multiply both sides by 2: 27 + 2t = 12 + t
Simplify: 27 + 2t - t = 12
27 + t = 12
t = 12 - 27
t = 12 - 14 = -2

At that time, Ella's age = 7 + -2 = 5
Verification: When Ella is 5, Kinsley 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

Let Jackson's current age = 31, Harsha's current age = 50
Given: When Jackson was born (0 years old), Harsha was 19 years old.
Therefore, Harsha is always 19 years older than Jackson.
So 50 = 31 + 19 ✓

Condition: Find t such that Jackson's age = ½ of Harsha's age
Equation: 31 + t = ½(50 + t)
Multiply both sides by 2: 231 + 2t = 50 + t
Simplify: 231 + 2t - t = 50
231 + t = 50
t = 50 - 231
t = 50 - 62 = -12

At that time, Jackson's age = 31 + -12 = 19
Verification: When Jackson is 19, Harsha 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

Let Neha's current age = 13, Amit's current age = 33
Given: When Neha was born (0 years old), Amit was 20 years old.
Therefore, Amit is always 20 years older than Neha.
So 33 = 13 + 20 ✓

Condition: Find t such that Neha's age = ½ of Amit's age
Equation: 13 + t = ½(33 + t)
Multiply both sides by 2: 213 + 2t = 33 + t
Simplify: 213 + 2t - t = 33
213 + t = 33
t = 33 - 213
t = 33 - 26 = 7

At that time, Neha's age = 13 + 7 = 20
Verification: When Neha is 20, Amit 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

Let Valentina's current age = 22, Kinsley's current age = 36
Given: When Valentina was born (0 years old), Kinsley was 14 years old.
Therefore, Kinsley is always 14 years older than Valentina.
So 36 = 22 + 14 ✓

Condition: Find t such that Valentina's age = ½ of Kinsley's age
Equation: 22 + t = ½(36 + t)
Multiply both sides by 2: 222 + 2t = 36 + t
Simplify: 222 + 2t - t = 36
222 + t = 36
t = 36 - 222
t = 36 - 44 = -8

At that time, Valentina's age = 22 + -8 = 14
Verification: When Valentina is 14, Kinsley 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