What is R5: Dividing in a ratio?

In a part:part ratio a:b, the whole contains a+b equal shares.

How many marks are R5 questions worth?

In verified past-paper appearances, R5 questions on Edexcel GCSE Maths 1MA1 have been worth 1–5 marks.

Which past exam papers has R5 appeared in?

R5 has appeared in 67 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

Divide a quantity in a given part:part or part:whole ratio; express division into two parts as a ratio; apply ratio to real problems (conversion, comparison, scaling, mixing, concentrations)

Dividing in a ratio

Worked answers, methods and verified real exam appearances for R5 on Edexcel GCSE Maths 1MA1.

Explanation

In a part:part ratio $a:b$ , the whole contains $a+b$ equal shares.
Divide the total by the sum of the ratio parts to find one share, then multiply by each part.
A part:whole statement needs different reading: if one part is $\dfrac{3}{8}$ of the whole, the other part is $\dfrac{5}{8}$ , giving ratio $3:5$ .
In mixing or concentration problems, track the amount of the relevant ingredient rather than simply averaging percentages.
Examiners expect both final parts to be labelled and to add back to the original total.

Worked example

A technician mixes a $20\%$ solution with a $50\%$ solution to make $18$ litres of a $40\%$ solution. Find the volume of each starting solution.

1.Let $x$ litres be the $50\%$ solution, so $18-x$ litres is the $20\%$ solution.
2.Equate solute amounts: $0.50x+0.20(18-x)=0.40\times18$ .
3. $0.30x=3.6$ , so $x=12$ and $18-x=6$ .

Answer: $12$ litres of the $50\%$ solution and $6$ litres of the $20\%$ solution.

Common mistakes

Don't divide the total by one ratio part instead of by the sum of all parts.
Don't treat a part:whole ratio as though both numbers were separate parts.
Don't average two concentrations without accounting for the volumes mixed.

Exam tip

Label each share or variable, then check that the parts sum to the stated whole.

Worked practice

Tier 1 · Easy

Divide £84 in the ratio

3:4

(2)

(Total for Question 1 is 2 marks)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	£36 and £48	2	There are $3+4=7$ shares, so one share is £ $84/7=£12$ . The two amounts are $3\times£12=£36$ and $4\times£12=£48$ .

Tier 2 · Standard

A box holds

240

counters. Red counters make up

\frac{3}{8}

of the whole. Find the number of red and non-red counters, and state their ratio.

(3)

(Total for Question 2 is 3 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	$90$ red counters $150$ non-red counters Ratio $3:5$	3	Red counters: $\frac{3}{8}\times240=90$ . The remainder is $240-90=150$ . Thus red:non-red is $90:150=3:5$ .

Tier 3 · Hard

Aisha and Ben share some money in the ratio

3:5

. Aisha gives £20 of her share to Ben. Their shares are now in the ratio

1:2

. Work out the total amount of money they shared.

(5)

(Total for Question 3 is 5 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	£480	5	Let the original shares be $3k$ pounds and $5k$ pounds. After the transfer, $2(3k-20)=5k+20$ , so $k=60$ . The original total was $8k=8\times60=£480$ .

Tier 1 · Easy

Two lengths are in the ratio

3:7

and differ by

28\,\text{cm}

. Work out the two lengths.

(2)

(Total for Question 4 is 2 marks)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$21\,\text{cm}$ and $49\,\text{cm}$	2	The difference of $7-3=4$ shares represents $28\,\text{cm}$ , so one share is $7\,\text{cm}$ . The lengths are $3\times7=21\,\text{cm}$ and $7\times7=49\,\text{cm}$ .

Tier 2 · Standard

Red, blue and white paint are mixed in the ratio

2:5:3

, and

1.8

litres of white paint is used. Work out the total volume of paint.

(3)

(Total for Question 5 is 3 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	$6$ litres	3	The $3$ white shares equal $1.8$ litres, so one share is $1.8\div3=0.6$ litres. There are $2+5+3=10$ shares, giving $10\times0.6=6$ litres in total.

Tier 3 · Hard

A drink is mixed using concentrate and water in the ratio

3:11

. Mia has

1.8

litres of concentrate and

7.2

litres of water. Work out the greatest volume of drink she can make.

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	$8.4$ litres	3	$1.8$ litres of concentrate needs $1.8\times\dfrac{11}{3}=6.6$ litres of water. Mia has enough water, so the concentrate is used up. The greatest volume is $1.8+6.6=8.4$ litres.

Tier 2 · Standard

A theatre sells

288

tickets. The ratio of adult tickets to child tickets is

7 : 5

. Adult tickets cost £11 and child tickets cost £7. Work out the total money received.

(4)

(Total for Question 7 is 4 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	£2688	4	There are $7+5=12$ shares, so one share is $288\div12=24$ tickets. There are $168$ adult tickets and $120$ child tickets. The total received is $168\times£11+120\times£7=£1848+£840=£2688$ .

Tier 3 · Hard

14

-litre fruit drink contains mango juice and apple juice in the ratio

2 : 5

. A different

12

-litre drink contains mango juice and apple juice in the ratio

1 : 3

. The two drinks are combined. Work out the ratio of mango juice to apple juice in the combined drink.

(4)

(Total for Question 8 is 4 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	$7 : 19$	4	The first drink contains $14\times\dfrac{2}{7}=4$ litres of mango and $10$ litres of apple. The second contains $12\times\dfrac{1}{4}=3$ litres of mango and $9$ litres of apple. The combined amounts are $7$ litres and $19$ litres, giving ratio $7 : 19$ .

Tier 3 · Hard

A fund is divided between A, B and C. A receives

\dfrac{2}{5}

of the whole fund. The rest is divided between B and C in the ratio

3 : 4

. C receives £840. Work out the value of the whole fund.

(4)

(Total for Question 9 is 4 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	£2450	4	B and C share $\dfrac{3}{5}$ of the fund. C receives $\dfrac{4}{7}$ of this remainder, so C receives $\dfrac{4}{7}\times\dfrac{3}{5}=\dfrac{12}{35}$ of the whole fund. The whole fund is £ $840\times\dfrac{35}{12}=£2450$ .

Q10

Tier 3 · Hard

A container holds

12

litres of a drink that is

30\%

concentrate. Water is added so that the new drink is

18\%

concentrate. Work out the volume of water added.

(4)

(Total for Question 10 is 4 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	$8$ litres	4	The amount of concentrate stays at $0.30\times12=3.6$ litres. If the final volume is $V$ litres, $0.18V=3.6$ , so $V=20$ . The volume of water added is $20-12=8$ litres.

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2024-11	2H	Q20	3	Allowed	Higher	QP MS
2023-06	1H	Q18	4	Non-calculator	Higher	QP MS
2024-06	2F	Q25	4	Allowed	Foundation	QP MS
2019-11	3H	Q13	4	Allowed	Higher	QP MS
2019-11	3F	Q16	4	Allowed	Foundation	QP MS
2022-11	3H	Q19	3	Allowed	Higher	QP MS
2024-06	3H	Q10	3	Allowed	Higher	QP MS
2019-06	2F	Q26	4	Allowed	Foundation	QP MS
2023-11	2F	Q26	4	Allowed	Foundation	QP MS
2019-11	1F	Q24	4	Non-calculator	Foundation	QP MS
2021-11	2H	Q11	5	Allowed	Higher	QP MS
2024-11	3F	Q21	5	Allowed	Foundation	QP MS
2022-11	3F	Q22	1	Allowed	Foundation	QP MS
2024-06	1F	Q26	5	Non-calculator	Foundation	QP MS
2019-11	3H	Q14	4	Allowed	Higher	QP MS
2024-11	2H	Q3	3	Allowed	Higher	QP MS
2019-06	3H	Q14	4	Allowed	Higher	QP MS
2023-11	1F	Q23	4	Non-calculator	Foundation	QP MS
2022-11	3H	Q17	4	Allowed	Higher	QP MS
2022-06	1F	Q25	5	Non-calculator	Foundation	QP MS
2021-11	1F	Q24	3	Non-calculator	Foundation	QP MS
2021-11	3H	Q14	4	Allowed	Higher	QP MS
2024-06	2H	Q6	4	Allowed	Higher	QP MS
2019-11	2H	Q3	4	Allowed	Higher	QP MS
2023-11	1H	Q6	4	Non-calculator	Higher	QP MS
2023-06	2F	Q22	1	Allowed	Foundation	QP MS
2022-11	1F	Q18	5	Non-calculator	Foundation	QP MS
2019-06	1H	Q2	5	Non-calculator	Higher	QP MS
2022-11	1F	Q17	5	Non-calculator	Foundation	QP MS
2022-06	2H	Q15	4	Allowed	Higher	QP MS
2024-06	2H	Q4	4	Allowed	Higher	QP MS
2019-06	2H	Q7	4	Allowed	Higher	QP MS
2023-11	2H	Q5	4	Allowed	Higher	QP MS
2022-06	2H	Q5	4	Allowed	Higher	QP MS
2021-11	1H	Q18	5	Non-calculator	Higher	QP MS
2019-06	2F	Q9	5	Allowed	Foundation	QP MS
2023-06	2H	Q3	1	Allowed	Higher	QP MS
2024-06	1H	Q7	5	Non-calculator	Higher	QP MS
2023-06	2F	Q25	3	Allowed	Foundation	QP MS
2023-06	2H	Q6	3	Allowed	Higher	QP MS
2021-11	3F	Q22	4	Allowed	Foundation	QP MS
2024-11	3H	Q5	5	Allowed	Higher	QP MS
2019-11	1H	Q5	4	Non-calculator	Higher	QP MS
2021-11	3H	Q2	4	Allowed	Higher	QP MS
2019-11	1H	Q2	4	Non-calculator	Higher	QP MS
2019-06	1F	Q27	4	Non-calculator	Foundation	QP MS
2019-06	3F	Q23	5	Allowed	Foundation	QP MS
2022-11	3F	Q20	4	Allowed	Foundation	QP MS
2024-06	2F	Q23	4	Allowed	Foundation	QP MS
2019-06	2H	Q19	4	Allowed	Higher	QP MS
2022-11	3H	Q4	4	Allowed	Higher	QP MS
2024-11	1F	Q17	3	Non-calculator	Foundation	QP MS
2019-11	1F	Q21	4	Non-calculator	Foundation	QP MS
2022-06	3H	Q18	5	Allowed	Higher	QP MS
2022-06	2F	Q25	4	Allowed	Foundation	QP MS
2022-11	3H	Q2	1	Allowed	Higher	QP MS
2024-06	3F	Q17	3	Allowed	Foundation	QP MS
2022-11	3F	Q24	4	Allowed	Foundation	QP MS
2019-06	1H	Q6	4	Non-calculator	Higher	QP MS
2021-11	3F	Q13	4	Allowed	Foundation	QP MS
2021-11	1H	Q5	3	Non-calculator	Higher	QP MS
2019-11	1H	Q11	2	Non-calculator	Higher	QP MS
2019-11	2F	Q23	4	Allowed	Foundation	QP MS
2023-06	3F	Q15	2	Allowed	Foundation	QP MS
2022-06	1H	Q3	5	Non-calculator	Higher	QP MS
2019-06	3F	Q28	4	Allowed	Foundation	QP MS
2019-11	3H	Q24	5	Allowed	Higher	QP MS

Other points in R Ratio, proportion and rates of change

Want help turning this into marks?

Bring R5 or any tricky specification point, and we can work through the method and exam wording together.

Book a free intro call