Two children share a prize in the ratio 3:5. The larger share is £8 more than the smaller share. What is the smaller share?
A) £8
B) £12
C) £16
D) £20
E) £24
(Total for Question 1 is 1 mark)
2
Two friends share a box of sweets in the ratio 7:3. The difference between their shares is 16 sweets. How many sweets does the larger friend receive?
A) 16
B) 21
C) 28
D) 32
E) 40
(Total for Question 2 is 1 mark)
3
Two pupils share stickers in the ratio 2:5. The larger pupil has 21 more stickers than the smaller. How many stickers does the smaller pupil have?
A) 7
B) 9
C) 14
D) 28
E) 35
(Total for Question 3 is 1 mark)
4
Two neighbours split vegetable plants in the ratio 4:9. The neighbour with the larger share has 15 more plants than the other. How many plants did they have altogether?
A) 21
B) 27
C) 36
D) 39
E) 66
(Total for Question 4 is 1 mark)
5
Two runners share prize money in the ratio 5:8. The larger share is £12 more than the smaller. How much does the larger runner receive?
A) £16
B) £20
C) £24
D) £32
E) £48
(Total for Question 5 is 1 mark)
6
A teacher divides reward points between two teams in the ratio 3:7. The larger team has 20 more points than the smaller. What is the total number of points?
A) 20
B) 35
C) 40
D) 50
E) 70
(Total for Question 6 is 1 mark)
7
Two friends share a bag of pens in the ratio 1:4. The larger share is 9 pens more than the smaller. How many pens does the smaller friend get?
A) 1
B) 3
C) 4
D) 6
E) 9
(Total for Question 7 is 1 mark)
8
The amounts Albert and Ben receive are in the ratio 2:3. Albert receives 5 pounds less than Ben. How many pounds does Albert receive?
A) £5
B) £7
C) £10
D) £15
E) £20
(Total for Question 8 is 1 mark)
9
Three children share a birthday cake in the ratio 2:3:5. The largest piece is 30 grams more than the smallest. What is the total mass of the cake in grams?
A) 50 g
B) 100 g
C) 150 g
D) 200 g
E) 1000 g
(Total for Question 9 is 1 mark)
10
Three projects receive funds in the ratio 1:2:4. The middle project receives 6 pounds more than the smallest. How many pounds does the smallest project receive?
A) £2
B) £3
C) £4
D) £6
E) £12
(Total for Question 10 is 1 mark)
11
Three siblings share savings in the ratio 3:4:7. The largest sibling gets £30 more than the middle sibling. How much does the smallest sibling receive?
A) £10
B) £20
C) £30
D) £40
E) £60
(Total for Question 11 is 1 mark)
12
Two children split apples in the ratio 4:5. The larger child has 9 more apples than the smaller. How many apples are there in total?
A) 18
B) 36
C) 45
D) 72
E) 81
(Total for Question 12 is 1 mark)
13
Sam and Priya share sweets in the ratio 7:2. Sam has 35 more sweets than Priya. How many sweets does Sam have?
A) 35
B) 42
C) 49
D) 70
E) 105
(Total for Question 13 is 1 mark)
14
A group divides a donation in the ratio 2:9. The larger share is £28 more than the smaller. What is the smaller share?
A) £4
B) £8
C) £16
D) £18
E) £36
(Total for Question 14 is 1 mark)
15
Two colleagues share commission in the ratio 6:11. The larger gets £25 more than the smaller. How much does the larger colleague receive?
A) £25
B) £33
C) £44
D) £55
E) £66
(Total for Question 15 is 1 mark)
16
A charity divides a sum in the ratio 3:8. The difference between the shares is £25. What is the total amount given out?
A) £25
B) £55
C) £65
D) £110
E) £275
(Total for Question 16 is 1 mark)
17
Two sisters share an inheritance in the ratio 5:7. The elder sister receives £4,200 more than the younger. Work out the smaller (younger) sister's share.
(Total for Question 17 is 2 marks)
18
A charity divides money between three projects A: B: C = 3: 4: 5. Project C receives £80 more than project A. Work out how much Project B receives.
(Total for Question 18 is 3 marks)
19
A cake is cut into four pieces in the ratio 1:2:3:4. The smallest piece is 150 grams less than the next smallest piece. Find the total mass of the cake in grams.
(Total for Question 19 is 4 marks)
20
Four people share prize money in the ratio 5:6:7:8. The person with 8 parts received £24 more than the person with 5 parts. Work out how much each person received.
(Total for Question 20 is 5 marks)
Mark scheme · EP.M103 Ratio Sharing when the Difference is Given
Question 1
B1 correct option B (£12) cao
Answer: B) £12 (smaller share = £12). The parts differ by 2, so 1 part = 8/2 = 4; smaller = 3 x 4 = 12. | Working check: distractors from common slips: A) assumes 1 part = 8, C) adds incorrectly, D/E) use wrong multiplier.
Question 2
B1 correct option C (28) cao
Answer: C) 28 sweets. One part = 16/4 = 4; larger = 7 x 4 = 28. | Working check: A) confuses difference with larger share; B/D) wrong division; E) uses total or sum error.
Question 3
B1 correct option C (14) cao
Answer: C) 14 stickers. Difference = 3 parts so 1 part = 21/3 = 7; smaller = 2 x 7 = 14. | Working check: A/B) divide difference incorrectly; D/E) multiply wrong part.
Question 4
B1 correct option D (39) cao
Answer: D) 39 plants. Difference is 5 parts so 1 part = 15/5 = 3; shares 12 and 27; total 39. | Working check: A/B/C) mix up parts or take one share only; E) total if 15 was 1 part misapplied.
Question 5
B1 correct option D (£32) cao
Answer: D) £32. Difference = 3 parts so 1 part = 12/3 = 4; larger = 8 x 4 = 32. | Working check: A/B/C) under-multiplying; E) uses sum of parts incorrectly.
Question 6
B1 correct option D (50) cao
Answer: D) 50 points. Difference = 4 parts so 1 part = 20/4 = 5; shares 15 and 35; total 50. | Working check: A/B/C) confusion between one share and difference; E) double counting.
Question 7
B1 correct option B (3) cao
Answer: B) 3 pens. Difference = 3 parts so 1 part = 9/3 = 3; smaller = 1 x 3 = 3. | Working check: A/C/D/E) common misdivisions or reading larger as 4 parts of 9.
Question 8
B1 correct option C (£10) cao
Answer: C) £10. Difference = 1 part so 1 part = 5; Albert = 2 x 5 = 10. | Working check: A/B) think 5 is total not 1 part; D/E) scale errors.
Question 9
B1 correct option B (100 g) cao
Answer: B) 100 g. Difference largest-smallest = 3 parts so 1 part = 30/3 = 10; total parts 2+3+5 = 10 so total mass = 10 x 10 = 100 g. | Working check: A/C/D) miscalculate parts; E) huge error.
Question 10
B1 correct option D (£6) cao
Answer: D) £6. Middle - smallest = 1 part so 1 part = 6; smallest = 1 x 6 = 6. | Working check: A/B/C) underestimate; E) total confusion.
Question 11
B1 correct option C (£30) cao
Answer: C) £30. Largest - middle = 7 - 4 = 3 parts, so 1 part = 30/3 = 10; smallest = 3 x 10 = 30. | Working check: distractors come from misidentifying which parts to use or using the wrong difference.
Question 12
B1 correct option E (81) cao
Answer: E) 81 apples. Difference = 1 part so 1 part = 9; shares 4x9 = 36 and 5x9 = 45; total 81. | Working check: A/B/C/D) common partial sums or one share only.
Question 13
B1 correct option C (49) cao
Answer: C) 49 sweets. Difference = 5 parts so 1 part = 35/5 = 7; Sam = 7 x 7 = 49. | Working check: A/B) misread difference; D/E) multiply total or all parts.
Question 14
B1 correct option B (£8) cao
Answer: B) £8. Difference = 9 - 2 = 7 parts, so 1 part = 28/7 = 4; smaller = 2 x 4 = 8. | Working check: distractors come from using the larger share or doubling the part value.
Question 15
B1 correct option D (£55) cao
Answer: D) £55. Difference = 5 parts so 1 part = 25/5 = 5; larger = 11 x 5 = 55. | Working check: A/B/C/E) common multiplication or division slips.
Question 16
B1 correct option C (£55) cao
Answer: C) £55. Difference = 5 parts so 1 part = 25/5 = 5; shares 15 and 40; total 55. | Working check: B/D/E) confusion with one share or mis-summing.
Question 17
M1 find 1 part = 4200/2 = 2100
A1 smaller share = 5 x 2100 = 10,500 cao
Answer: £10,500 (younger sister). Working check: difference = 7-5 = 2 parts so 1 part = 4200/2 = 2100; younger = 5 x 2100 = £10,500.
Question 18
M1 recognise difference C-A = 2 parts and find 1 part = 80/2 = 40
M1 calculate B = 4 x 40 = 160
A1 160 cao
Answer: £160. Working check: C-A = 5-3 = 2 parts so 1 part = 80/2 = 40; B = 4 x 40 = 160.
Question 19
M1 identify difference between 2nd smallest and smallest = 1 part
M1 find 1 part = 150 g
M1 calculate total parts = 1+2+3+4 = 10 and method to find total mass
A1 total = 150 x 10 = 1500 g cao
Answer: 1500 g. Working check: 2nd smallest - smallest = 2-1 = 1 part = 150 g. Total parts 10 so 150 x 10 = 1500 g.
Question 20
M1 recognise difference 8-5 = 3 parts
M1 find 1 part = 24/3 = 8
M1 calculate at least two individual amounts using 1 part
M1 calculate remaining amounts correctly
A1 full correct set: 40, 48, 56, 64 cao
Answer: They received £40, £48, £56 and £64 respectively. Working check: 8-5 = 3 parts so 1 part = 24/3 = 8. Then 5x8 = 40, 6x8 = 48, 7x8 = 56, 8x8 = 64.