Age at Event | Worksheet 3/10 - Beginner skill builder ⚡

Question 1

When Nikolai was born, Neelam was 22 years old. The sum of their present ages is 90. Find Nikolai's age when Nikolai was half of Neelam's age (this will happen 12 years ago).

Let Nikolai's current age = 34, Neelam's current age = 56
Given: When Nikolai was born (0 years old), Neelam was 22 years old.
Therefore, Neelam is always 22 years older than Nikolai.
So 56 = 34 + 22 ✓

Condition: Find t such that Nikolai's age = ½ of Neelam's age
Equation: 34 + t = ½(56 + t)
Multiply both sides by 2: 234 + 2t = 56 + t
Simplify: 234 + 2t - t = 56
234 + t = 56
t = 56 - 234
t = 56 - 68 = -12

At that time, Nikolai's age = 34 + -12 = 22
Verification: When Nikolai is 22, Neelam 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 2

When Layla was born, Ishwar was 7 years old. The sum of their present ages is 39. Find Layla's age when Layla was half of Ishwar's age (this will happen 9 years ago).

Let Layla's current age = 16, Ishwar's current age = 23
Given: When Layla was born (0 years old), Ishwar was 7 years old.
Therefore, Ishwar is always 7 years older than Layla.
So 23 = 16 + 7 ✓

Condition: Find t such that Layla's age = ½ of Ishwar's age
Equation: 16 + t = ½(23 + t)
Multiply both sides by 2: 216 + 2t = 23 + t
Simplify: 216 + 2t - t = 23
216 + t = 23
t = 23 - 216
t = 23 - 32 = -9

At that time, Layla's age = 16 + -9 = 7
Verification: When Layla is 7, Ishwar 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 3

When Jitendra was born, Isaac was 16 years old. The sum of their present ages is 42. Find Jitendra's age when Jitendra was half of Isaac's age (this will happen in 3 years).

Let Jitendra's current age = 13, Isaac's current age = 29
Given: When Jitendra was born (0 years old), Isaac was 16 years old.
Therefore, Isaac is always 16 years older than Jitendra.
So 29 = 13 + 16 ✓

Condition: Find t such that Jitendra's age = ½ of Isaac's age
Equation: 13 + t = ½(29 + t)
Multiply both sides by 2: 213 + 2t = 29 + t
Simplify: 213 + 2t - t = 29
213 + t = 29
t = 29 - 213
t = 29 - 26 = 3

At that time, Jitendra's age = 13 + 3 = 16
Verification: When Jitendra is 16, Isaac 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 4

When Gajendra was born, Felix was 6 years old. The sum of their present ages is 16. Find Gajendra's age when Gajendra was half of Felix's age (this will happen in 1 years).

Let Gajendra's current age = 5, Felix's current age = 11
Given: When Gajendra was born (0 years old), Felix was 6 years old.
Therefore, Felix is always 6 years older than Gajendra.
So 11 = 5 + 6 ✓

Condition: Find t such that Gajendra's age = ½ of Felix's age
Equation: 5 + t = ½(11 + t)
Multiply both sides by 2: 25 + 2t = 11 + t
Simplify: 25 + 2t - t = 11
25 + t = 11
t = 11 - 25
t = 11 - 10 = 1

At that time, Gajendra's age = 5 + 1 = 6
Verification: When Gajendra is 6, Felix 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 Chetan was born, Claire was 17 years old. The sum of their present ages is 47. Find Chetan's age when Chetan was half of Claire's age (this will happen in 2 years).

Let Chetan's current age = 15, Claire's current age = 32
Given: When Chetan was born (0 years old), Claire was 17 years old.
Therefore, Claire is always 17 years older than Chetan.
So 32 = 15 + 17 ✓

Condition: Find t such that Chetan's age = ½ of Claire's age
Equation: 15 + t = ½(32 + t)
Multiply both sides by 2: 215 + 2t = 32 + t
Simplify: 215 + 2t - t = 32
215 + t = 32
t = 32 - 215
t = 32 - 30 = 2

At that time, Chetan's age = 15 + 2 = 17
Verification: When Chetan is 17, Claire 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 6

When Sonam was born, Autumn was 24 years old. The sum of their present ages is 48. Find Sonam's age when Sonam was half of Autumn's age (this will happen in 12 years).

Let Sonam's current age = 12, Autumn's current age = 36
Given: When Sonam was born (0 years old), Autumn was 24 years old.
Therefore, Autumn is always 24 years older than Sonam.
So 36 = 12 + 24 ✓

Condition: Find t such that Sonam's age = ½ of Autumn's age
Equation: 12 + t = ½(36 + t)
Multiply both sides by 2: 212 + 2t = 36 + t
Simplify: 212 + 2t - t = 36
212 + t = 36
t = 36 - 212
t = 36 - 24 = 12

At that time, Sonam's age = 12 + 12 = 24
Verification: When Sonam is 24, Autumn 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

Question 7

When Nirmala was born, Tristan was 25 years old. The sum of their present ages is 65. Find Nirmala's age when Nirmala was half of Tristan's age (this will happen in 5 years).

Let Nirmala's current age = 20, Tristan's current age = 45
Given: When Nirmala was born (0 years old), Tristan was 25 years old.
Therefore, Tristan is always 25 years older than Nirmala.
So 45 = 20 + 25 ✓

Condition: Find t such that Nirmala's age = ½ of Tristan's age
Equation: 20 + t = ½(45 + t)
Multiply both sides by 2: 220 + 2t = 45 + t
Simplify: 220 + 2t - t = 45
220 + t = 45
t = 45 - 220
t = 45 - 40 = 5

At that time, Nirmala's age = 20 + 5 = 25
Verification: When Nirmala is 25, Tristan 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 Hana was born, Bella was 19 years old. The sum of their present ages is 55. Find Hana's age when Hana was half of Bella's age (this will happen in 1 years).

Let Hana's current age = 18, Bella's current age = 37
Given: When Hana was born (0 years old), Bella was 19 years old.
Therefore, Bella is always 19 years older than Hana.
So 37 = 18 + 19 ✓

Condition: Find t such that Hana's age = ½ of Bella's age
Equation: 18 + t = ½(37 + t)
Multiply both sides by 2: 218 + 2t = 37 + t
Simplify: 218 + 2t - t = 37
218 + t = 37
t = 37 - 218
t = 37 - 36 = 1

At that time, Hana's age = 18 + 1 = 19
Verification: When Hana is 19, Bella 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 9

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

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

Condition: Find t such that Gautam's age = ½ of Jivika'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, Gautam's age = 5 + 5 = 10
Verification: When Gautam is 10, Jivika 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 10

When Dhara was born, Neeraj was 6 years old. The sum of their present ages is 30. Find Dhara's age when Dhara was half of Neeraj's age (this will happen 6 years ago).

Let Dhara's current age = 12, Neeraj's current age = 18
Given: When Dhara was born (0 years old), Neeraj was 6 years old.
Therefore, Neeraj is always 6 years older than Dhara.
So 18 = 12 + 6 ✓

Condition: Find t such that Dhara's age = ½ of Neeraj's age
Equation: 12 + t = ½(18 + t)
Multiply both sides by 2: 212 + 2t = 18 + t
Simplify: 212 + 2t - t = 18
212 + t = 18
t = 18 - 212
t = 18 - 24 = -6

At that time, Dhara's age = 12 + -6 = 6
Verification: When Dhara is 6, Neeraj 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 11

When Maverick was born, Yash was 11 years old. The sum of their present ages is 23. Find Maverick's age when Maverick was half of Yash's age (this will happen in 5 years).

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

Condition: Find t such that Maverick's age = ½ of Yash's age
Equation: 6 + t = ½(17 + t)
Multiply both sides by 2: 26 + 2t = 17 + t
Simplify: 26 + 2t - t = 17
26 + t = 17
t = 17 - 26
t = 17 - 12 = 5

At that time, Maverick's age = 6 + 5 = 11
Verification: When Maverick is 11, Yash 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 12

When Ujjwal was born, Jaxson was 4 years old. The sum of their present ages is 36. Find Ujjwal's age when Ujjwal was half of Jaxson's age (this will happen 12 years ago).

Let Ujjwal's current age = 16, Jaxson's current age = 20
Given: When Ujjwal was born (0 years old), Jaxson was 4 years old.
Therefore, Jaxson is always 4 years older than Ujjwal.
So 20 = 16 + 4 ✓

Condition: Find t such that Ujjwal's age = ½ of Jaxson's age
Equation: 16 + t = ½(20 + t)
Multiply both sides by 2: 216 + 2t = 20 + t
Simplify: 216 + 2t - t = 20
216 + t = 20
t = 20 - 216
t = 20 - 32 = -12

At that time, Ujjwal's age = 16 + -12 = 4
Verification: When Ujjwal is 4, Jaxson is 8 = 8
Check: Is 4 = ½ × 8? ½ × 8 = 4.0 ✓

Note: Mathematically, this always equals the age difference (4) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 13

When Tushar was born, Caleb was 15 years old. The sum of their present ages is 63. Find Tushar's age when Tushar was half of Caleb's age (this will happen 9 years ago).

Let Tushar's current age = 24, Caleb's current age = 39
Given: When Tushar was born (0 years old), Caleb was 15 years old.
Therefore, Caleb is always 15 years older than Tushar.
So 39 = 24 + 15 ✓

Condition: Find t such that Tushar's age = ½ of Caleb's age
Equation: 24 + t = ½(39 + t)
Multiply both sides by 2: 224 + 2t = 39 + t
Simplify: 224 + 2t - t = 39
224 + t = 39
t = 39 - 224
t = 39 - 48 = -9

At that time, Tushar's age = 24 + -9 = 15
Verification: When Tushar is 15, Caleb 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 14

When Shikha was born, Peter was 11 years old. The sum of their present ages is 21. Find Shikha's age when Shikha was half of Peter's age (this will happen in 6 years).

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

Condition: Find t such that Shikha's age = ½ of Peter's age
Equation: 5 + t = ½(16 + t)
Multiply both sides by 2: 25 + 2t = 16 + t
Simplify: 25 + 2t - t = 16
25 + t = 16
t = 16 - 25
t = 16 - 10 = 6

At that time, Shikha's age = 5 + 6 = 11
Verification: When Shikha is 11, Peter 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 15

When Lokesh was born, Devanshi was 8 years old. The sum of their present ages is 18. Find Lokesh's age when Lokesh was half of Devanshi's age (this will happen in 3 years).

Let Lokesh's current age = 5, Devanshi's current age = 13
Given: When Lokesh was born (0 years old), Devanshi was 8 years old.
Therefore, Devanshi is always 8 years older than Lokesh.
So 13 = 5 + 8 ✓

Condition: Find t such that Lokesh's age = ½ of Devanshi's age
Equation: 5 + t = ½(13 + t)
Multiply both sides by 2: 25 + 2t = 13 + t
Simplify: 25 + 2t - t = 13
25 + t = 13
t = 13 - 25
t = 13 - 10 = 3

At that time, Lokesh's age = 5 + 3 = 8
Verification: When Lokesh is 8, Devanshi 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 16

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

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

Condition: Find t such that Balram's age = ½ of Katia'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, Balram's age = 18 + 4 = 22
Verification: When Balram is 22, Katia 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 17

When Arlo was born, Jaya was 17 years old. The sum of their present ages is 77. Find Arlo's age when Arlo was half of Jaya's age (this will happen 13 years ago).

Let Arlo's current age = 30, Jaya's current age = 47
Given: When Arlo was born (0 years old), Jaya was 17 years old.
Therefore, Jaya is always 17 years older than Arlo.
So 47 = 30 + 17 ✓

Condition: Find t such that Arlo's age = ½ of Jaya's age
Equation: 30 + t = ½(47 + t)
Multiply both sides by 2: 230 + 2t = 47 + t
Simplify: 230 + 2t - t = 47
230 + t = 47
t = 47 - 230
t = 47 - 60 = -13

At that time, Arlo's age = 30 + -13 = 17
Verification: When Arlo is 17, Jaya 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 18

When Urvashi was born, Rajiv was 16 years old. The sum of their present ages is 58. Find Urvashi's age when Urvashi was half of Rajiv's age (this will happen 5 years ago).

Let Urvashi's current age = 21, Rajiv's current age = 37
Given: When Urvashi was born (0 years old), Rajiv was 16 years old.
Therefore, Rajiv is always 16 years older than Urvashi.
So 37 = 21 + 16 ✓

Condition: Find t such that Urvashi's age = ½ of Rajiv's age
Equation: 21 + t = ½(37 + t)
Multiply both sides by 2: 221 + 2t = 37 + t
Simplify: 221 + 2t - t = 37
221 + t = 37
t = 37 - 221
t = 37 - 42 = -5

At that time, Urvashi's age = 21 + -5 = 16
Verification: When Urvashi is 16, Rajiv 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 19

When Sourav was born, Ishika was 12 years old. The sum of their present ages is 60. Find Sourav's age when Sourav was half of Ishika's age (this will happen 12 years ago).

Let Sourav's current age = 24, Ishika's current age = 36
Given: When Sourav was born (0 years old), Ishika was 12 years old.
Therefore, Ishika is always 12 years older than Sourav.
So 36 = 24 + 12 ✓

Condition: Find t such that Sourav's age = ½ of Ishika's age
Equation: 24 + t = ½(36 + t)
Multiply both sides by 2: 224 + 2t = 36 + t
Simplify: 224 + 2t - t = 36
224 + t = 36
t = 36 - 224
t = 36 - 48 = -12

At that time, Sourav's age = 24 + -12 = 12
Verification: When Sourav is 12, Ishika 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 20

When Amit was born, Kumud was 13 years old. The sum of their present ages is 69. Find Amit's age when Amit was half of Kumud's age (this will happen 15 years ago).

Let Amit's current age = 28, Kumud's current age = 41
Given: When Amit was born (0 years old), Kumud was 13 years old.
Therefore, Kumud is always 13 years older than Amit.
So 41 = 28 + 13 ✓

Condition: Find t such that Amit's age = ½ of Kumud's age
Equation: 28 + t = ½(41 + t)
Multiply both sides by 2: 228 + 2t = 41 + t
Simplify: 228 + 2t - t = 41
228 + t = 41
t = 41 - 228
t = 41 - 56 = -15

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

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