Question 1
1(a) If the ratio of x:y is 6:11, and x=27,
what is the value of y?
ANSWER: Multiple Choice (Type 1)
A: 32
B: 33
C: 49.5
D: 55
Answer: C
Workings:
\dfrac{27}{6} = 4.5
4.5 \times 11 = 49.5
Marks = 1
1(b) If 200 grams of one ingredient is used in a recipe, which calls for a ratio of 4:7 with a second ingredient, how much of the second ingredient is needed?
ANSWER: Multiple Choice (Type 1)
A: 203 grams
B: 280 grams
C: 350 grams
D: 1400 grams
Answer: C
Workings:
\dfrac{200}{4} = 50
50 \times 7 = 350
Marks = 1
1(c) In a class of 42 students, the ratio of male : female is 2:4.
How many females are there?
ANSWER: Multiple Choice (Type 1)
A: 14
B: 28
C: 40
D: 42
Answer: A
Workings:
2 + 4 = 6
\dfrac{42}{6} = 7
7 \times 4 = 28
Marks = 1
Question 2
Consider the following table:
2(a) Complete the table for the missing values.
ANSWER: Multiple Answers (Type 1)
Answer: A = 119, B = 57
Workings:
Ratio of table is \dfrac{7}{3}
\dfrac{51}{3} = 17
A = 17 \times 7 = 119
\dfrac{133}{7} = 19
B = 19 \times 3 = 57
Marks = 2
2(b) Express the ratio x:y in simplest form.
ANSWER: Simple text answer
Answer: 3:7
Workings:
(12:28) \div 4 = 3:7
Marks = 2
Question 3
There are 200 medals bought for a sports celebration.
The ratio of winning medals to participation medals is 1:4.
3(a) How many of each of the winning and participation medals are there?
ANSWER: Multiple Answers (Type 1)
Answer: Winning medals = 40
Participation medals = 160
Workings:
1 + 4 = 5
\dfrac{200}{5} = 40
40 \times 4 = 160
Ratio = 40:160
Marks = 2
3(b) An additional 40 medals are purchased.
The ratio of winning medals to participation medals remains at 1:4.
Find the number of winning and participation medals there would be after the 40 medals are added.
ANSWER: Multiple Answers (Type 1)
Answer:
Winning medals = 48
Participation Medals = 192
Workings:
\dfrac{240}{5} = 48
48 \times 4 = 192
Ratio = 48:192
Marks = 2
Question 4
Terry, Alisha and Ella run on a weekly basis.
In total, they average 176 km a week.
If Alisha runs twice as far as Terry and Ella runs one third of Alisha’s distance, how far do each of them run?
ANSWER: Multiple Answers (Type 1)
Answer: Terry = 48 km
Alisha = 96 km
Ella = 32 km
Workings:
Ratio = 3:6:2
3 + 6 + 2 = 11
\dfrac{176}{11} = 16
16 \times 3 = 48
16 \times 6 = 96
16 \times 2 = 32
Marks = 3
Question 5
A construction company needs workers for a job.
The ratio of general labour to management is 8:1
The budget for each general labourer is £2,500 and £8,200 for each management employee.
There are 32 general labourers employed.
How much is spent on all the employees for the job?
ANSWER: Multiple Answers (Type 1)
Answer:
Total = \pounds112,800
Workings:
32 \times \pounds2,500 = \pounds80,000
\dfrac{32}{8} = 4
4 \times \pounds8,200 =\pounds 32,800
Total = \pounds80,000 + \pounds32,800 = \pounds112,800
Marks = 3
Question 6
There is £80 in a pot which is shared out amongst 3 people.
Anne gets £20, Mark gets £35 and Ben gets £25.
What ratio of the money does each person receive?
ANSWER: Multiple Answers (Type 1)
Answer:
Anne = 4
Mark = 7
Ben = 5
Workings:
(20:35:25) \div 5 = 4:7:5
Marks = 2
Question 7
210 cakes are shared out in a ratio of 1:2:3 in to groups a, b and c respectively.
How many cakes does each group receive?
ANSWER: Multiple Answers (Type 1)
Answer
Group a = 35
Group b = 70
Group c = 105
Workings:
1 + 2 + 3 = 6
\dfrac{210}{6} = 35
35 \times 2 = 70
35 \times 3 = 105
Marks = 2
Question 8
£60 pocket money is split between three people.
Sally gets twice the amount of Rob and Malik gets three times more than Rob.
8(a):
How much money does each person get?
ANSWER: Multiple Answers (Type 1)
Answer:
Sally = \pounds20
Rob = \pounds10
Malik = \pounds30
Workings:
Ratio Sally : Rob : Malik = 2:1:3
2 + 1 + 3 = 6
\dfrac{60}{6} = 10
2 \times 10 = 20
3 \times = 30
Marks = 2
8(b):
How much does each person get if the original amount is reduced by 50%?
ANSWER: Multiple Answers (Type 1)
Sally = \pounds10
Rob = \pounds5
Malik = \pounds15
Workings:
\dfrac{10}{2} = 5
\dfrac{20}{2} = 10
\dfrac{30}{2} = 15
Marks = 2
Question 9
There are 24 people working in a kitchen,
4 men below the age of 18,
4 women below the age of 18,
8 women above the age of 18
8 men above the age of 18
9(a):
What proportion of the people in the kitchen were male?
Give your answer as a fraction in its simplest form.
ANSWER: Fraction
Answer = \dfrac{1}{2}
Workings:
4 + 8 = 12
\dfrac{12}{24} = \dfrac{1}{2}
Marks = 1
9(b):
Find the ratio of women below the age of 18, compared to the total numbers of workers in the kitchen.
Give your answer in its simplest form.
ANSWER: Simple Text Answer
Answer = 1:5
Workings:
\dfrac{4}{24} = \dfrac{1}{6}
Ratio = 1:5
Marks = 2