GCSE / IGCSE Maths – Ratio and Proportion
Ratio, direct and inverse proportion, compound measures, growth and decay.
This worksheet covers:
- Simplifying and sharing in a ratio
- Direct and inverse proportion
- Compound measures (speed, density, pressure)
- Percentage change
- Compound interest
- Growth
- Decay
Section A is non-calculator; a calculator may be used in Sections B and C. Allow about 50 minutes.
Questions
Write each ratio in its simplest form.(a) $18 : 24$(b) $0.5 : 2.5$(c) $2.4\,\text{kg} : 600\,\text{g}$
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Share 840 pounds between Amy, Ben and Cara in the ratio $3 : 4 : 5$.
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Given that $a : b = 2 : 3$ and $b : c = 4 : 5$, find $a : b : c$.
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A recipe for 4 people uses 300 g of flour and 2 eggs. How much flour and how many eggs are needed for 10 people?
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Priya and Sam share some money in the ratio $5 : 2$. Priya receives 36 pounds more than Sam. How much money did they share in total?
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$y$ is directly proportional to the square of $x$. When $x = 4$, $y = 48$.(a) Find a formula for $y$ in terms of $x$.(b) Find $y$ when $x = 5$.(c) Find the positive value of $x$ when $y = 108$.
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(a) It takes 6 identical pumps 20 minutes to empty a tank. How long would it take 8 such pumps?(b) $p$ is inversely proportional to the square root of $q$. When $q = 25$, $p = 8$. Find $p$ when $q = 16$.
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(a) A train travels 150 km in 2 hours 30 minutes. Find its average speed in km/h.(b) How long does a car take to travel 210 km at an average speed of 84 km/h?(c) Convert 60 km/h to metres per second. Give your answer to 3 significant figures.
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(a) A block of metal has mass 540 g and volume 200 cm$^3$. Find its density in g/cm$^3$.(b) A force of 600 N acts on an area of $0.4\,\text{m}^2$. Find the pressure in N/m$^2$.
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(a) 2500 pounds is invested at 3.2 percent per year compound interest. Find the value of the investment after 4 years. Give your answer to the nearest penny.(b) A car bought for 18 000 pounds loses 15 percent of its value each year. Find its value after 3 years.
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The population of a town is 1.2 million and is increasing by 2.5 percent each year. After how many whole years will the population first exceed 1.5 million?
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(a) In a class the ratio of boys to girls is $3 : 5$. When 4 more boys join the class the ratio becomes $4 : 5$. How many students were in the class originally?(b) The exchange rate is 1 pound $= 1.15$ euros. A jacket costs 276 euros in France and 245 pounds in the UK. In which country is it cheaper, and by how many pounds?
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