Ratio & Proportion (Cambridge (CIE) IGCSE Maths: Core)

Alan and Beth share $1190 in the ratio Alan : Beth = 5 : 2.

Work out how much Alan receives.

$..........................

Alex and Chris share sweets in the ratio Alex : Chris = 7 : 3.
Alex receives 20 more sweets than Chris.

Work out the number of sweets Chris receives.

One week the café makes a profit of $1027.
George, Louis and Beatriz share this profit in the ratio George : Louis : Beatriz = 7 : 4 : 2.

Calculate the amount of money they each receive.

  George $ ......................................................
Louis   $ ......................................................
Beatriz $ ......................................................

Alexa, Ben and Chloe share the profits from their restaurant in the ratio 2 : 6 : 7.
One year the restaurant makes a profit of $60000.

Work out how much each receives.

Alexa = $ .................................................
Ben = $ .................................................
Chloe = $ ................................................. 

Share 518 in the ratio 2 : 5.

Here is a list of ingredients to make 12 pancakes.

Complete the list of ingredients below to make 30 pancakes.

Asif and Ben share $2100 in the ratio Asif : Ben = 3 : 7.

Work out how much Asif receives.

$ ......................................... 

Zach is looking at the costs of a holiday.

The ratio of the costs flights : hotels = 3 : 8.
The cost of the flights is $861.

Work out the total cost of flights and hotels.

$ ................................................... 

The music teacher at a school forms an orchestra.
The instruments in the orchestra are 36 string, 15 woodwind and 12 brass.

Write the ratio string : woodwind : brass in its simplest form.

................ : ................ : ................ 

The 36 string instruments are violins, cellos and double basses in the ratio

violins : cellos : double basses = 9 : 2 : 1.

i) Show that the number of violins is 27.

[1]

ii) Work out the number of cellos and the number of double basses.

Cellos ..........................     
Double basses ........................... [2]

A car park has 880 parking spaces.

Some of the spaces are reserved.
The ratio of reserved spaces : not reserved spaces = 1 : 10.

Work out the number of spaces that are not reserved.

Gabriela designs the seating layout for a new theatre.
There are three sections of seats, A, B and C.

Section A has 152 seats.
Section B has 171 seats.
Section C has 57 seats.

Write down and simplify the ratio of the number of seats in each section A : B : C.

A : B : C = ............. : ............. : ............. 

For a concert in the theatre, the ticket prices are in the ratio

A : B : C = 9 : 7 : 4.

A ticket for Section C costs $6.

i) Show that a ticket for Section B costs $10.50 .

[1]

ii) Find the cost of a ticket for Section A.

$ .................................................. [1]

iii) The table shows the number of tickets sold in each section.

Calculate the total amount received from the ticket sales.

$ .................................................. [3]

iv) The concert costs $4500 to organise. 

Calculate the amount received from the ticket sales as a percentage of the $4500.

[1]

A bag contains yellow balls, pink balls and green balls only.

The ratio yellow balls : pink balls : green balls = 7 : 3 : 5.
There are 42 yellow balls in the bag.

Work out the total number of balls in the bag.

100 g of cereal contains 360 kilocalories.
100ml of milk contains 45 kilocalories.
For breakfast Sasha has 35 g of cereal with 180ml of milk.

Work out the number of kilocalories Sasha has for breakfast.

.......................................... kcal

A shop sells cereal in boxes A, B and C.

Work out which box is the best value.
You must show all your working.

Box ................................................. 

A bag contains red marbles, green marbles and blue marbles only.
The ratio of the number of marbles of each colour is

red : green : blue = 12 : 5 : 2.

There are 112 more red marbles than green marbles.

Work out the number of blue marbles.

A farmer has 45 horses and 20 cows.

i) Write this as a ratio of horses : cows.
Give your answer in its simplest form.

[1]

ii) The farmer wants the ratio of horses : cows to equal 5 : 3.
He keeps his 45 horses and buys some more cows.

Work out the number of cows he must buy.

[2]

Nadira has some T-shirts that are either white or blue or green. The numbers of T-shirts are in the ratio white : blue : green = 5 : 4 : 1. 48 of the T-shirts are blue.

Work out the total number of T-shirts.

Raoul makes a profit when he sells his watch for $36.
The ratio of the price Raoul paid for the watch and the profit he makes is price paid : profit = 7 : 2.

Work out the profit that Raoul makes.

$....................................................