A and B share a bag of sweets in the ratio 2:3. What fraction of the sweets does A receive?
A) 2/3
B) 2/5
C) 3/5
D) 1/3
E) 1/5
(Total for Question 1 is 1 mark)
2
There are 20 students in a club. The ratio of boys to girls is 4:1. How many girls are there?
A) 4
B) 5
C) 8
D) 16
E) 12
(Total for Question 2 is 1 mark)
3
A and B share money in the ratio 5:3. If A receives £25, how much does B receive?
A) £10
B) £15
C) £20
D) £30
E) £40
(Total for Question 3 is 1 mark)
4
A recipe uses flour and sugar in the ratio 3:2. If the total mixture is 25 g, how much sugar is used?
A) 5 g
B) 7.5 g
C) 10 g
D) 12.5 g
E) 15 g
(Total for Question 4 is 1 mark)
5
Amy has 3/7 of a cake and Ben has the rest. What is the ratio Amy:Ben?
A) 3:4
B) 3:7
C) 4:3
D) 3:10
E) 7:3
(Total for Question 5 is 1 mark)
6
Three friends share £60 in the ratio 2:3:1. How much does the middle friend receive?
A) £10
B) £15
C) £20
D) £30
E) £35
(Total for Question 6 is 1 mark)
7
Alfie and Priya share sweets in the ratio 7:5. They have 48 sweets in total. How many sweets does Priya have?
A) 14
B) 16
C) 20
D) 25
E) 30
(Total for Question 7 is 1 mark)
8
A mixture contains alcohol and water in the ratio 1:9. What fraction of the mixture is alcohol?
A) 1/9
B) 1/10
C) 1/5
D) 9/10
E) 1/8
(Total for Question 8 is 1 mark)
9
There are 24 tiles in two colours in the ratio red:blue = 5:1. How many red tiles are there?
A) 4
B) 5
C) 12
D) 20
E) 18
(Total for Question 9 is 1 mark)
10
A and B share money in the ratio 4:7. After A receives an extra £24, the ratio becomes 5:8. How much did A have originally?
(Total for Question 10 is 2 marks)
11
A bowl contains sugar and water in the ratio 2:5. When 21 g of water is added the ratio becomes 2:7. How much sugar was in the bowl originally?
(Total for Question 11 is 2 marks)
12
Three drinks A, B and C are mixed in the ratio 3:4:5. The total mixture is 480 ml. How much of drink B is used?
(Total for Question 12 is 2 marks)
13
A wins 3/8 of a prize fund of £240. The remaining money is split between B and C in the ratio 2:3. How much does C receive?
(Total for Question 13 is 2 marks)
14
Two numbers are in the ratio 2:5. If 9 is added to each number, the ratio becomes 11:14. Find the original two numbers.
(Total for Question 14 is 2 marks)
15
A and B share money in the ratio 5:3. A gives £6 to B and the new ratio becomes 7:5. How much did A have originally?
(Total for Question 15 is 2 marks)
16
A, B and C share an amount. A has 1/3 of the total and B has 1/4 of the total. What is the ratio A:B:C?
(Total for Question 16 is 2 marks)
17
B pays A £12 so that after the payment the ratio of A:B becomes 3:4. Before the payment A and B were in the ratio 2:3. How much money did A have at the start?
(Total for Question 17 is 3 marks)
18
A, B and C share £480 in the ratio 4:5:7. C is then given an extra £30 (from outside) so that C's new amount becomes twice A's original amount. What was A's original share?
(Total for Question 18 is 3 marks)
19
Two numbers are in the ratio 2:7. If 6 is added to each number the ratio becomes 4:9. Find the original two numbers.
(Total for Question 19 is 3 marks)
20
A pile of cards is split into three piles in the ratio 4:6:9. The middle pile has 30 more cards than the smallest pile. How many cards were there in the pile originally?
(Total for Question 20 is 3 marks)
Mark scheme · EP.M106 Combined Ratio and Fraction Problems
Question 1
B1 correct option B (2/5) cao
Answer: B) 2/5 (A receives 2 out of 5 equal parts of the sweets.) The total ratio parts = 2+3 = 5 so A has 2/5 of the sweets. (Distractors: A) swapped parts; C) B's fraction; D) 1/3 arises from confusion with thirds; E) 1/5 is a place-value slip.)
Question 2
B1 correct option A (4) cao
Answer: A) 4 (Total parts 4+1 = 5, each part = 20/5 = 4, girls = 1 part = 4.)
Question 3
B1 correct option B (£15) cao
Answer: B) £15 (One part = 25/5 = £5, B has 3 parts = 3 x £5 = £15.)
Question 4
B1 correct option C (10 g) cao
Answer: C) 10 g (Total parts 3+2 = 5 so sugar = 2/5 of 25 = 10 g.)
Question 5
B1 correct option A (3:4) cao
Answer: A) 3:4 (Amy has 3/7 so Ben has 4/7; ratio Amy:Ben = 3:4.)
Question 6
B1 correct option D (£30) cao
Answer: D) £30 (Total parts 2+3+1=6, each part = £60/6 = £10, middle friend 3 parts = £30.)
Question 7
B1 correct option C (20) cao
Answer: C) 20 (Total parts 7+5 = 12, one part = 48/12 = 4, Priya has 5 parts = 5 x 4 = 20.)
Question 8
B1 correct option B (1/10) cao
Answer: B) 1/10 (Total parts 1+9 = 10, alcohol is 1 out of 10 parts.)
Question 9
B1 correct option D (20) cao
Answer: D) 20 (Total parts 5+1 = 6, one part = 24/6 = 4, red = 5 x 4 = 20.)
Question 10
M1 form equation (4k + 24)/(7k) = 5/8 or equivalent method
A1 £256 cao
Answer: £256 (Let A = 4k, B = 7k. (4k + 24)/(7k) = 5/8 gives 32k + 192 = 35k so k = 64, A = 4k = 256.)
Question 11
M1 use 2k/(5k + 21) = 2/7 or equivalent and solve for k
A1 21 g cao
Answer: 21 g (2k/(5k + 21) = 2/7 => 7*2k = 2*(5k + 21) => 14k = 10k + 42 => k = 10.5, sugar = 2k = 21 g.)
Question 12
M1 find one part = 480/12 or equivalent
A1 160 ml cao
Answer: 160 ml (Total parts 3+4+5 = 12, one part = 480/12 = 40, B = 4 x 40 = 160 ml.)
Question 13
M1 calculate remainder after A: 240 - (3/8 x 240) = 150 or equivalent
A1 £90 cao
Answer: £90 (A = 3/8 x £240 = £90, remainder £150 split 2:3 so C gets 3/5 of 150 = £90.)
Question 14
M1 form equation (2k + 9)/(5k + 9) = 11/14 or equivalent
A1 2 and 5 cao
Answer: 2 and 5 (Solve 14(2k + 9) = 11(5k + 9) giving k = 1, so numbers 2k = 2 and 5k = 5.)
Question 15
M1 form equation (5k - 6)/(3k + 6) = 7/5 or equivalent
A1 £90 cao
Answer: £90 (Solve 5(5k - 6) = 7(3k + 6) gives k = 18 so A = 5k = £90.)
Question 16
M1 convert fractions to common denominator and express amounts as integers (e.g. 4/12, 3/12, 5/12)
A1 4:3:5 cao
Answer: 4:3:5 (A = 1/3 = 4/12, B = 1/4 = 3/12, rest = 5/12 so ratio 4:3:5.)
Question 17
M1 let A = 2k, B = 3k and form equation (2k + 12)/(3k - 12) = 3/4 or equivalent
M1 solve linear equation to find k = 84
A1 £168 cao
Answer: £168 (Let A = 2k, B = 3k. After B pays A £12: (2k + 12)/(3k - 12) = 3/4. Solve 4(2k + 12) = 3(3k - 12): 8k + 48 = 9k - 36 so k = 84. A = 2k = £168.)
Question 18
M1 use total to find k (480 = 16k) or use equation 7k + 30 = 2 x 4k to find k
M1 solve k = 30
A1 £120 cao
Answer: £120 (Let shares 4k, 5k, 7k. From 7k + 30 = 2(4k) we get k = 30, so A = 4k = £120. Check: total 16k = £480.)
Question 19
M1 form equation (2k + 6)/(7k + 6) = 4/9 or equivalent
M1 solve 9(2k + 6) = 4(7k + 6) leading to k = 3
A1 6 and 21 cao
Answer: 6 and 21 (Let numbers be 2k and 7k. 9(2k + 6) = 4(7k + 6) gives k = 3 so numbers 2k = 6 and 7k = 21.)
Question 20
M1 let one unit = x so 6x - 4x = 30 and form equation 2x = 30
M1 solve x = 15 and compute total units 4+6+9 = 19
A1 285 cao
Answer: 285 cards (If one unit = x then middle minus smallest = 6x - 4x = 2x = 30 so x = 15. Total = 19x = 19 x 15 = 285.)