IGCSE Maths Ratio, proportion, rates topical questions

A fruit punch uses orange juice and mango juice in the ratio 4 : 3.

1. (a)How much orange juice is mixed with 630 ml of mango juice?[2]
2. (b)How much punch does this make, in litres?[2]

A cyclist rides 24 km at an average speed of 16 km/h.

1. (a)Calculate the time taken, in hours.[2]
2. (b)Write this time in hours and minutes.[1]

Petrol costs 1.68 per litre.

1. (a)Find the cost of 12.5 litres.[2]
2. (b)A driver pays 42.00. How many litres did they buy?[1]

Amir and Bella share 120 in the ratio 5 : 3.

1. (a)Find Bella’s share.[2]
2. (b)Find how much more Amir receives than Bella.[2]
3. (c)Amir saves 25% of his share. Find his savings.[1]

A jogger runs 8.4 km in 70 minutes.

1. (a)Find the jogger’s average speed in km/h.[3]
2. (b)At the same speed, how many minutes would a 10.8 km run take?[2]

A bronze sculpture is made from copper, tin and zinc in the ratio 17 : 3 : 1.

1. (a)Find the mass of copper in a 4.2 kg sculpture.[2]
2. (b)How much more copper than zinc does the sculpture contain? Give your answer in grams.[3]

Two shops sell the same rice: Shop A sells 5 kg bags at 14.50; Shop B sells 2 kg bags at 6.20.

1. (a)Which shop is better value? Show your working.[2]
2. (b)How much cheaper is 20 kg of rice at the better shop than at the other?[2]

A city of 8 400 000 people covers 1200 km².

1. (a)Find the population density, in people per km².[2]
2. (b)A neighbouring district has the same population density but covers 95 km². Estimate its population.[2]

A map has a scale of 1 : 25 000.

1. (a)A lake covers 3.2 cm² on the map. Find its real area in square kilometres.[3]
2. (b)A walking route is 12 km long. Find its length on the map, in centimetres.[2]

A granola recipe for 8 people uses 300 g of oats and 120 g of honey.

1. (a)Find the mass of oats needed for 14 people.[2]
2. (b)Show that the recipe uses 0.4 g of honey for every gram of oats.[2]
3. (c)A bigger batch uses 450 g of oats. Find the honey needed.[1]

The stopping distance d of a car is directly proportional to the square of its speed v. A car moving at 30 km/h has a stopping distance of 18 m. (Extended)

1. (a)Find an equation for d in terms of v.[3]
2. (b)Find the stopping distance at 50 km/h.[2]
3. (c)A second car needs 32 m to stop. Find its speed, correct to 1 decimal place.[1]

A tap fills a 225-litre tank in 15 minutes. A second tap, running at three quarters of the first tap’s rate, is used instead. (Extended)

1. (a)Find the flow rate of the first tap, in litres per minute.[1]
2. (b)How long does the second tap take to fill the tank, in minutes and seconds?[3]
3. (c)Both taps run together from empty. How long do they take to fill the tank? Give your answer correct to the nearest second.[3]

The time t hours to paint a fence is inversely proportional to the number of painters n. Three painters take 8 hours. (Extended)

1. (a)Write an equation for t in terms of n.[2]
2. (b)Find t when four painters share the job.[1]
3. (c)How many painters are needed for the job to take 4 hours?[1]
4. (d)Explain why the job can never take exactly 7 hours with a whole number of painters.[2]

A cyclist rides 54 km at 27 km/h, rests for 20 minutes, then rides 30 km at 20 km/h.

1. (a)Find the total riding time, in hours.[2]
2. (b)Find the average speed for the whole outing, including the rest, correct to 3 significant figures.[3]
3. (c)Sponsors pay 0.50 for each kilometre ridden. Show that the ride raises more than 40.[2]