
Initial Diagnostic Audit  Unit A4: Ratio and Proportion
Do NOT use a calculator for any questions in the audit unless specifically told otherwise 
Section A4.1  Simple Proportion 
1. 
Simplify the ratio 35 : 14. :

2. 
A class comprises 15 girls and 12 boys.
What is the ratio of girls to boys, in its simplest form? :

3. 
A drink contains 60 cm^{3} of which 10 cm^{3} is fruit concentrate and the remainder water.
What is the ratio of concentrate to water? :

4. 
The ratio of teachers to students in a school is 1 : 12.
If there are 9 teachers, how many students are there in the school?

5. 
In a packet of nibbles there are peanuts and raisins in the ratio 2 : 3.
How many peanuts are there in a packet that contains 24 raisins?

Section A4.2  Ratio and Proportion 
6. 
The ratio of the length to the width of a picture is 5 : 3.
If the picture is 45 cm in length, what is its width? cm 
7. 
The ratio of flour to sugar in a recipe is 7 : 2.
How much flour should be mixed with 50 g of sugar? g

8. 
5 kg of potatoes cost £2.30.
What is the cost of 8 kg of potatoes? £ 
9. 
200 g of flour are needed to make 15 shortbread biscuits.
(a) What is the weight of flour needed to make 36 shortbread biscuits? g
(b) How many shortbread biscuits can be made using 1.6 kg of flour? 
Section A4.3  Map Scales and Ratios 
10. 
The distance between two towns is 20 km.
What is the distance, in cm, between these two towns on a map with the scale 1 : 40000? cm 
11. 
A map has scale 1 : 25000.
What actual distance does a map distance of 8 cm represent? km 
12. 
Two places are 6.4 km apart. On a map they are 16 cm apart.
What is the scale of the map? :

13. 
On a map with a scale of 1 : 300000, the distance between Bristol and Bath is 6 cm.
Find the distance between these two towns on a map with scale 1 : 240000. cm 
14. 
On a map with a scale of 1 : 50000, a plot of land is represented by a rectangle 1.6 cm by 1.2 cm.
What is the actual area of the plot of land? km^{2} 
Section A4.4  Proportional Division 
15. 
The ratio of boys to girls in a school choir is 3 : 5.
How many boys are in the choir if there are 64 members in total? 
16. 
Chris, Tim and Jamie share 240 stickers between them in the ratio 3 : 2 : 1.
How many stickers does Tim have? km 
17. 
Apples, bananas and oranges are mixed in the ratio 3 : 4 : 5 respectively, by weight, to make a fruit salad.
(a) If there are 800 g of bananas in the fruit salad, what is the total weight of the fruit salad? g
(b) What weight of apples would be needed to make 2 kg of fruit salad? g

18. 
A fruit corner yogurt weighs 175 g altogether. If the packaging weighs 13 g and the weight of fruit to the weight of yogurt is in
the ratio 2 : 7, calculate the weight of the fruit. g 