> ## Content Index > Fetch the complete content index at: https://www.a-level-maths-tutor.com/llms.txt > Use this file to discover other available public pages before exploring further. # GCSE Maths | Ratios - URL: https://www.a-level-maths-tutor.com/gcse-maths-ratios/ - Published: 2026-07-22T14:28:40.000Z - Updated: 2026-07-22T14:50:00.000Z - Author: Jaisul Naik - Tags: GCSE Maths # Simple Ratios **Worked Example** Share £40 in the ratio 3:5 $3 : 5 \\quad (8)$ $? : ? \\quad (40)$ $sf = 40 \\div 8 = 5$ $3 \\times 5 = 15, \\quad 5 \\times 5 = 25$ ## Question 1 **a)** Share £20 in the ratio 2:3 **b)** Share 15cm in the ratio 1:2 **c)** Divide £24 in the ratio 1:3 **d)** Share 35 sweets in the ratio 4:3 **e)** Divide 55g in the ratio 3:2 **f)** Divide 54kg in the ratio 1:5 **g)** Share £104 in the ratio 3:5 **h)** Divide 161 miles in the ratio 6:1 **i)** Divide 315ml in the ratio 2:7 **j)** Share $650 in the ratio 4:9 **k)** Share £800 in the ratio 11:14 **l)** Share 1200kg in the ratio 3:37 Show Answers **a)** £8, £12 **b)** 5cm, 10cm **c)** £6, £18 **d)** 20, 15 sweets **e)** 33g, 22g **f)** 9kg, 45kg **g)** £39, £65 **h)** 138, 23 miles **i)** 70ml, 245ml **j)** $200, $450 **k)** £352, £448 **l)** 90kg, 1110kg # Applying Ratios **Worked Example** The ratio of cats to dogs in a shelter is 3:4\. There are 12 cats. How many dogs are there? $3 : 4$ $12 : ?$ $sf = 12 \\div 3 = 4$ Dogs $= 4 \\times 4 = 16$ ## Question 2 **a)** James has some apples and oranges. The ratio of apples to oranges is 2:5\. He has 15 oranges. How many apples does James have? **b)** The ratio of lemon sweets to strawberry sweets in a tub is 5:3\. There are 120 lemon sweets in the tub. How many strawberry sweets are in the tub? **c)** Rachel has some first class and some second class stamps. The ratio of first class to second class stamps is 3:4\. Rachel has 18 first class stamps. (i) How many second class stamps does Rachel have? (ii) How many stamps does Rachel have in total? **d)** Abby, Neil and Dylan share a sum of money in the ratio 2:4:5\. Neil receives £60\. Work out how much money Dylan receives. **e)** Isaac and Victoria share money in the ratio 2:5\. Victoria receives £6.60\. Work out the difference between how much money Isaac and Victoria receive. **f)** Rachel has some apples and bananas. The ratio of apples to bananas is 2:3\. She has 14 apples. Work out how many bananas Rachel has. **g)** Chris and Molly win money in a competition. They share the money in the ratio 2:3\. Molly receives £240\. How much money does Chris receive? **h)** The ratio of boys to girls in a school is 4:5\. There are 220 boys in the school. How many students attend the school? **i)** Three angles are in the ratio 2:3:5\. The smallest angle is 50°. Work out the sizes of the other two angles. Show Answers **a)** 6 apples **b)** 72 strawberry sweets **c)** (i) 24 second class stamps (ii) 42 stamps in total **d)** £75 **e)** £3.96 **f)** 21 bananas **g)** £160 **h)** 495 students **i)** 75° and 125° # Comparing Ratios If you know the difference between two shares, that difference corresponds to a whole number of parts. Divide the difference by that number of parts to find one share. **Worked Example** Sam and Tia share sweets in the ratio 2:5\. Tia gets 18 more sweets than Sam. How many sweets does each person get? Difference in parts $= 5-2 = 3$ One share $= 18 \\div 3 = 6$ Sam $= 2 \\times 6 = 12$, Tia $= 5 \\times 6 = 30$ ## Question 3 **a)** Charlene and Danielle share some money in ratio 2:3\. Danielle gets £25 more than Charlene. How much does each girl receive? **b)** The costs of building a single-storey house extension are in the ratio labour : materials : professional fees $= 7:5:1$. The cost of materials is £6,400 more than the amount paid in professional fees. Work out the total cost of building this house extension. **c)** Three quantities $A$, $B$ and $C$ are in the ratio $A:B:C$ is $13:7:2$. Given that $A - B = 48$, find the value of $A + B + C$. **d)** Last season, the number of goals scored by Arjun, by Simon and by Kath for their football team were in the ratios 2:5:8\. Simon scored 12 more goals than Arjun. Work out the number of goals scored by Kath. Show Answers **a)** Charlene: £50, Danielle: £75 **b)** £20,800 **c)** $A+B+C = 176$ **d)** $32$ goals # Combining Ratios **Worked Example** $a:b = 2:3$ and $b:c = 6:5$. Find $a:b:c$. $a:b = 4:6$ and $b:c = 6:5$ $a:b:c = 4:6:5$ ## Question 4 Combine the following ratios, or find $a:b:c$. **a)** $a:b$ is $3:2$ and $b:c$ is $2:5$ **b)** $a:b$ is $3:1$ and $b:c$ is $2:3$ **c)** $a:b$ is $7:4$ and $b:c$ is $2:1$ **d)** $a:b$ is $2:3$ and $b:c$ is $2:5$ **e)** $a:b$ is $9:2$, $b:c$ is $6:7$, and $a+b+c = 200$. Find $a$, $b$ and $c$. Show Answers **a)** $a:b:c = 3:2:5$ **b)** $a:b:c = 6:2:3$ **c)** $a:b:c = 7:4:2$ **d)** $a:b:c = 4:6:15$ **e)** $a = 135$, $b = 30$, $c = 35$ # Ratios and Equations **Worked Example (ratio to equation)** $a:b = 4:7$ $7a = 4b$ **Worked Example (equation to ratio)** $3a = 8b$ $a:b = 8:3$ ## Question 5 Turn each ratio into an equation. **a)** $a:b = 6:5$ **b)** $a:b = 3:4$ **c)** $a:b = 7:2$ **d)** $a:b = 5:9$ **e)** $a:b = 8:3$ Turn each equation into a ratio $a:b$. **f)** $6a = 5b$ **g)** $4a = 9b$ **h)** $3a = 7b$ **i)** $2a = 5b$ **j)** $5a = 8b$ Show Answers **a)** $5a = 6b$ **b)** $4a = 3b$ **c)** $2a = 7b$ **d)** $9a = 5b$ **e)** $3a = 8b$ **f)** $a:b = 5:6$ **g)** $a:b = 9:4$ **h)** $a:b = 7:3$ **i)** $a:b = 5:2$ **j)** $a:b = 8:5$ --- ### GCSE Maths Tutoring I offer one-to-one and small group GCSE Maths tutoring for students across the UK and internationally. 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