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11+ · Algebra and Number

EP.M114 Age and Difference Problems

GL ASSESSMENT GL-11PLUS-MATHS · Calculators not allowed · about 55 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Yusuf is 12 years older than his sister. His sister is 9 years old. What is Yusuf's age now?

A) 3
B) 12
C) 18
D) 21
E) 9

(Total for Question 1 is 1 mark)

Priya is three times as old as her brother. The sum of their ages is 48. Work out Priya's age now.

(Total for Question 2 is 1 mark)

Amelia is twice as old as her brother now. In 3 years time the sum of their ages will be 51. Find their current ages.

(Total for Question 3 is 2 marks)

Kwame is 8 years older than Erin. Erin is 14 years old. How old is Kwame now?

(Total for Question 4 is 1 mark)

A father is 4 times as old as his child now. In 6 years time the father will be 3 times as old as the child. Find their current ages.

(Total for Question 5 is 2 marks)

The total of three siblings' ages is 38. The oldest is twice as old as the middle sibling. The youngest is 2 years younger than the middle sibling. Find the three ages now.

(Total for Question 6 is 2 marks)

Sam is 5 times as old as Lara. Lara is 3 years old. How old is Sam?

A) 8
B) 15
C) 20
D) 18
E) 5

(Total for Question 7 is 1 mark)

The difference between a parent and their child is 9 years. In 7 years time the parent will be twice as old as the child. Find their current ages.

(Total for Question 8 is 2 marks)

The sum of the ages of four friends is 71. Ben is the youngest. Anne is 2 years older than Ben. Cara is 3 years younger than Anne. Dan is twice as old as Ben. Find each person's age now.

(Total for Question 9 is 3 marks)

Ten years ago a mother was 5 times as old as her daughter was then. The sum of their ages now is 50. Find their current ages.

(Total for Question 10 is 2 marks)

Tom is 4 years older than twice Sam's age. Tom is 22 years old. How old is Sam now?

A) 9
B) 11
C) 8
D) 10
E) 7

(Total for Question 11 is 1 mark)

Two years ago the sum of a couple's ages was 80. Now the younger is 4 years younger than the older. Find their current ages.

(Total for Question 12 is 2 marks)

A grandmother is three times as old as her grandchild now. In 12 years time she will be twice as old as the grandchild. Find their current ages.

(Total for Question 13 is 3 marks)

Three siblings have consecutive even-numbered ages. The sum of their ages is 78. Work out the three ages.

(Total for Question 14 is 2 marks)

A father is 40 years old and he is 4 times as old as his son. How old is the son?

A) 9
B) 10
C) 12
D) 8
E) 11

(Total for Question 15 is 1 mark)

The sum of A and B's ages is 31. Five years ago A was twice as old as B was then. Find A and B's current ages.

(Total for Question 16 is 3 marks)

In 9 years time a mother will be three times as old as her daughter will be then. The mother is currently 39 years old. How old is the daughter now?

(Total for Question 17 is 2 marks)

Three people have ages in the ratio 5: 3: 2 and their total age is 80. Work out each person's age.

(Total for Question 18 is 3 marks)

A is 7 years older than B now. In 4 years time the ages of A and B will be in the ratio 3: 2. Find their current ages.

(Total for Question 19 is 2 marks)

An aunt is 6 times as old as her nephew now. In 6 years time she will be 4 times as old as him then. Find their current ages.

(Total for Question 20 is 2 marks)

Mark scheme · EP.M114 Age and Difference Problems

Question 1

B1 correct option D (21) cao
Answer: D) 21 years old (9 + 12 = 21).

Question 2

B1 36 cao
Answer: 36 years old (let brother = x, Priya = 3x, 4x = 48 so x = 12 and Priya = 36).

Question 3

M1 Equation set up: let brother = b, Amelia = 2b, then (2b+3) + (b+3) = 51 seen
A1 brother 15 and Amelia 30 cao
Answer: Brother 15 years, Amelia 30 years (3b + 6 = 51 => b = 15).

Question 4

B1 22 cao
Answer: 22 years old (14 + 8 = 22).

Question 5

M1 Let child = c, father = 4c; equation 4c + 6 = 3(c + 6) seen
A1 child 12 and father 48 cao
Answer: Child 12 years, father 48 years (4c + 6 = 3c + 18 => c = 12).

Question 6

M1 Let middle = m so ages 2m, m, m-2 and equation 2m + m + (m - 2) = 38 seen
A1 ages 20, 10, 8 cao
Answer: Oldest 20, middle 10, youngest 8 (4m - 2 = 38 => m = 10).

Question 7

B1 correct option B (15) cao
Answer: B) 15 years old (5 x 3 = 15).

Question 8

M1 Let child = x, parent = x + 9; equation x + 9 + 7 = 2(x + 7) seen
A1 child 2 and parent 11 cao
Answer: Child 2 years, parent 11 years (x = 2).

Question 9

M1 Let Ben = b and express others: Anne b+2, Cara b-1, Dan 2b and form sum 5b + 1 = 71 seen
M1 Solve 5b + 1 = 71 to get b = 14
A1 Give ages Ben 14, Anne 16, Cara 13, Dan 28 cao
Answer: Ben 14, Anne 16, Cara 13, Dan 28 (5b + 1 = 71 => b = 14).

Question 10

M1 Let daughter = d, mother = m; use m - 10 = 5(d - 10) and m + d = 50 to form equations seen
A1 daughter 15 and mother 35 cao
Answer: Daughter 15, mother 35 (m = 5d - 40, substitute m + d = 50 gives d = 15).

Question 11

B1 correct option A (9) cao
Answer: A) 9 years old (2s + 4 = 22 => 2s = 18 => s = 9).

Question 12

M1 Let older = p and younger = p - 4; use (p - 2) + (p - 4 - 2) = 80 or 2p - 8 = 80 seen
A1 current ages 44 and 40 cao
Answer: Older 44, younger 40 (2p - 8 = 80 => p = 44).

Question 13

M1 Let grandchild = g and grandmother = 3g; equation 3g + 12 = 2(g + 12) seen
M1 Rearrange to get g = 12
A1 grandchild 12 and grandmother 36 cao
Answer: Grandchild 12, grandmother 36 (3g + 12 = 2g + 24 => g = 12).

Question 14

M1 Let smallest even = n then n, n+2, n+4 and equation 3n + 6 = 78 seen
A1 ages 24, 26, 28 cao
Answer: 24, 26, 28 years (3n + 6 = 78 => n = 24).

Question 15

B1 correct option B (10) cao
Answer: B) 10 years old (40 ÷ 4 = 10).

Question 16

M1 Let B = b and A = a; use a + b = 31 and a - 5 = 2(b - 5) to form equations
M1 Substitute a = 2b - 5 into a + b = 31 and solve 3b = 36
A1 A = 19 and B = 12 cao
Answer: A = 19 years, B = 12 years (a = 2b - 5, 3b = 36 => b = 12).

Question 17

M1 Let daughter = d; set up 39 + 9 = 3(d + 9) seen
A1 daughter 7 cao
Answer: 7 years old (48 = 3(d + 9) => d + 9 = 16 => d = 7).

Question 18

M1 Recognise total ratio parts 5 + 3 + 2 = 10 and form 10k = 80
M1 Find unit k = 8 and multiply ratio parts
A1 ages 40, 24, 16 cao
Answer: 40, 24, 16 years (k = 8 so 5k = 40, 3k = 24, 2k = 16).

Question 19

M1 Let B = b and A = b + 7; set up (b + 7 + 4)/(b + 4) = 3/2
A1 A = 17 and B = 10 cao
Answer: A 17, B 10 years (2(b + 11) = 3(b + 4) => b = 10).

Question 20

M1 Let nephew = n and aunt = 6n; equation 6n + 6 = 4(n + 6) seen
A1 nephew 9 and aunt 54 cao
Answer: Nephew 9, aunt 54 (6n + 6 = 4n + 24 => 2n = 18 => n = 9).

Age and Difference Problems - Worksheets, Questions and Revision