Ratio, Proportion, Rates and Percentages

122.
Express 250 g to 2 kg as ratio in its simplest form.
................................. [2]
Paper 1
123.
Matseliso has a cake. She gives 2 7 of it to Teboho and 1 6 of it to Thato.
Find the fraction of the cake left, giving your answer in its simplest form.
.................................
Paper 1
124.
In a class, the ratio of boys to girls is 3:5. There are 15 boys in the class.
Find:
(a) the number of students in the class
......................... [2]
(b) the percentage of girls
......................... [2]
Paper 1
125.
The picture is drawn to the scale of 1:250.

The height of the tree in the picture is 3 cm.
Find the actual height of the tree in metres.
................................. m [2]
Paper 1
126.
Express 9 20 as a percentage.
.................................
Paper 1
127.
Express 20 cm to 1 m as ratio, in its simplest form.
................................. [2]
Paper 1
128.
In a class, the ratio of boys to girls is 3:5. There are 15 boys in the class. Find the number of students in the class.
................................. [2]
Paper 1
129.
12% of 5 8
.................................
Paper 1
130.
Express 12 cm as a percentage of 4 m.
................................. [2]
Paper 1
131.
Write the ratio 5.5 : 2.5 in its simplest form.
................................. [2]
Paper 1
132.
x : y = 3 : 7 and y : z = 2 : 3
Find the ratio x : y : z
................................. [3]
Paper 1
133.
Simplify the ratio: 1 1 3 : 0.78
................................. [2]
Paper 1
134.
When 20 kg of carrots are peeled, 1 kg is lost as peel.
Find the percentage loss.
................................. % [2]
Paper 1
71.
20 litres of drink contains a concentrate and 40% of water.
(i) Write the ratio of water to concentrate in its simplest form.
......................... [2]
(ii) Calculate the volume of water that must be added if the new mixture of drink contains 70% of water.
......................... litres [3]
Paper 3
72.
In a street of 180 houses, 90 of them have one occupant, 45 have two occupants, 36 have three occupants, and the rest have four or more occupants.
(a) What percentage of houses has fewer than four occupants?
......................... [1]
(b) What percentage of houses has four or more occupants?
......................... [1]
Paper 3
73.
Three friends share M180.00. Limpho gets M54.00, Joalane gets M81.00 and Atang the rest.
What percentage of the total amount of money does each receive?
Limpho: ......................... Joalane: ......................... Atang: ......................... [3]
Paper 3
74.
Unemployment figures at the end of the last quarter increased by 725 000. If the increase in the number of unemployed this quarter is 7.5% fewer than the last quarter, calculate the increase in the number of people unemployed this quarter.
......................... [2]
Paper 3
75.
60% of students in a class are girls. The rest are boys.
(a) What is the proportion of girls to boys, in its lowest terms?
......................... [1]
(b) What fraction of the same class are boys?
......................... [1]
(c) If there are 30 students in the class altogether, how many are girls?
......................... [1]
Paper 3
76.
The ratio of the angles of a triangle is 1:2:3. What is the size of the smallest angle?
......................... [2]
Paper 3
77.
It takes 30 hours for three people to dig a trench.
(a) How long will it take:
(i) four people?
......................... hours [1]
(ii) five people?
......................... hours [1]
(b) How many people would it take to dig a trench in:
(i) 15 hours?
......................... [1]
(ii) 45 hours?
......................... [1]
Paper 3
78.
A metal cube of side 3 cm has a mass of 2700 g.
(a) What is its density? (Mass = Volume × Density)
......................... g/cm3 [2]
(b) What would be the mass of a similar cube of side 2.5 cm?
......................... g [3]
Paper 3