 Exam-Style Questions on Ratio

Problems on Ratio adapted from questions set in previous Mathematics exams.

1.

GCSE Higher

At a concert, the number of men, women and children can be expressed with the following ratio:

$$6 : 11 : 4$$

There were 6525 more women than men. How many children were at the concert?

2.

GCSE Higher

Mrs Painter makes a large amount of orange paint by mixing red and yellow paint in the ratio 3 : 4.

• Red paint costs £70 for 14 litres.
• Yellow paint costs £49 for 14 litres. Mrs Painter sells her orange paint in 14-litre tins for £62 per tin.

Calculate how much profit she makes for each tin she sells.

3.

GCSE Higher

Toystore sell model sheep in four different colours. In their newest warehouse there are currently 1760 sheep in stock. Three eighths of the sheep are yellow, 15% of the sheep are blue and the ratio of green to red sheep is 5:6.    Work out the number of sheep of each colour in the Toystore warehouse.

4.

IGCSE Extended

In January, a supermarket sold 12 624 boxes of breakfast cereal.

(a) The cost of a box of cereal was £2.15 . Calculate the amount received from the sale of the 12 624 boxes. Give your answer correct to the nearest hundred pounds.

(b) The number of boxes sold in February was 13% more than the number sold in January. Calculate the number of boxes sold in February. (c) There were 3 different types of cereal. The number of boxes sold of each type every month was in the ratio Riceflakes : Cornflakes : Branflakes = 4 : 5 : 3. The total number of boxes sold was 12 624. Calculate the number of boxes of Branflakes sold.

(d) How may more boxes of Cornflakes than Riceflakes were sold in February?

(e) $$\frac{5}{6}$$ of the 12 624 bottles sold in January are included in a special promotion. Calculate the number of boxes that are included in that promotion.

5.

GCSE Higher

Promise is going to make some chocolate pyramids to sell.

The ingredients are chocolate, honey butter and cornflakes. The ingredients are mixed in the ratio $$5:2:3$$ respectively.

(a) How much of each ingredient will she need to make 800g of the mixture?

• A bar of chocolate weighs 200g and costs £2.80.
• A jar of honey butter contains 320g and costs £1.90.
• A packet of cornflakes contains 300 g and costs £2.40.

Promise makes 3.2 kg of the mixture, from which she can make 80 chocolate pyramids.

She charges 70p for each pyramid and sells all 80 of them.

(b) How much profit does she make?

6.

GCSE Higher

An Airbus A380 plane is used by Tran Tours to fly between Dubai and London and holds a maximum of 740 passengers. The seating has been configured so that 15% of the seats are business class and the rest are economy class.

On one full flight, the ratio of males to females was 3:2. One eigth of the females were in business class.

How many males were in economy class? 7.

GCSE Higher

The ratio a : b is equivalent to the ratio 7 : 3 and 8b = 5c

Find the ratio a : c in its simplest form.

8.

GCSE Higher

At a summer camp the campers can choose one of three programmes: camp craft, water sports or hiking.

During the first week of camp the campers chose the programmes in the ratio 7 : 5 : 8

During the second week of camp the same number of campers chose the programmes in the ratio 7 : 6 : 4

Show that there were more campers on the camp craft programme in the second week than the first.

9.

GCSE Higher

The points A, B C and D lie in order on a straight line.

$$AB:BD = 1:4$$ $$AC:CD = 9:11$$

Using the information above calculate the three part ratio:

$$AB:BC:CD$$

10.

GCSE Higher

The prices of two watches are in the ratio $$a:b$$.

When the prices are both increased by £10, the ratio becomes $$5 : 7$$.

When the prices are both reduced by £10, the ratio becomes $$1 : 3$$.

Express the ratio $$a:b$$ in its lowest terms.

11.

GCSE Higher

The surface gravity, $$g$$, of a planet is the gravitational acceleration experienced at its surface. The following formula can be used to find how a planet's gravity compares to Earth's.

$$g=\frac{6.67 \times 10^{-11} \times m}{r^2}$$

Where $$m$$ is the mass of the planet and $$r$$ is the radius.

Find the ratio of the surface gravity on Jupiter and the surface gravity Mars. Give your answer in the form $$n:1$$.

 Mass (kg) Radius (m) Jupiter 1.90 × 1027 6.68 × 107 Mars 6.39 × 1023 3.39 × 106

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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