How to Pass Numerical Reasoning (38 page)

Proportions practice questions

Solve these questions by setting up a proportion and solving for the missing term.

Q1
In a swimming lesson, there are 4 swimming teachers for every 24 children. How many teachers should there be if there are 36 children in the pool?

Q2
In an evening class, the ratio of students studying Russian to students studying Chinese is 4 : 5. There are 81 students registered to study either Russian or Chinese. How many are studying Chinese?

Q3
A computer image measuring 180 pixels in height and 240 pixels in width is enlarged proportionately. After the enlargement, the picture measures 540 pixels in height. What is its width?

Q4
If four keyboards cost $99, how much do five keyboards cost?

Q5
Find the missing term in the proportion 3 : 9 =
x
: 18.

Q6
If 12 doughnuts cost £1.80, how much do 15 doughnuts cost?

Q7
If it takes Emma 10 minutes to do 60 sit-ups, how many minutes (M) does it take her to do S sit-ups?

Q8
Simplify the ratio 16
x
²
: 4
x
²
.

Q9
The ratio of carers to residents in a residential care home is 1 : 6. If an extension is built to the main building, an additional 40 residents will be accepted. If all 40 places are allocated and the number of carers remains constant, there will be eight times as many residents as carers. How many carers are there currently?

Q10
In a race, for every mountain bike there are 20 road bikes. If an additional 200 road bikers were to join the race, there would be 25 times as many road bikes as mountain bikes in the race. How many road bikes and mountain bikes are there at the beginning of the race?

Answers to Chapter 5

Ratios converter drill 1

Q1
1 : 4

Q2
6 : 5

Q3
4 : 1

Q4
1 : 1

Q5
4 : 5

Q6
6 : 1

Q7
7 : 3

Q8
23 : 24

Q9
7 : 9

Q10
23 : 17

Ratios converter drill 2

Ratios practice questions

Q1
32 : 1

Q2
1 : 2

Q3
16 : 9

Q4
5 : 6

Q5
3 : 2

Q6
8 : 11

Q7
119 : 120

Q8
1 : 3

Q9
1 : 2 : 5

Q10
17 : 28

Q11
1375 miles

Q12
£180

Q13
15 games

Q14
2 hours

Q15
240 : 1

Ratios practice questions explanations

Q1
Answer
= 32 : 1

Recall the formula: