1. 1
   A charity shares a donation of paint between two schools in a given ratio and needs to express and use ratios correctly.

   (a)

   Simplify the ratio $24:36$ to its simplest form.

   [1 mark]

   • A$2:3$
   • B$3:4$
   • C$4:6$
   • D$1:2$

   (b)

   Write the ratio $2:3$ in the form $1:n$.

   [1 mark]

   • A$1:3$
   • B$1:2$
   • C$1:1.5$
   • D$1:0.67$

   (c)

   A donation of 500 litres of paint is shared between two schools in the ratio $2:3$. How many litres does the school with the larger share receive?

   [1 mark]

   • A$150$ litres
   • B$200$ litres
   • C$250$ litres
   • D$300$ litres

   Total for question 1: 3 marks

2. 2
   A drinks company mixes mango juice and water in a fixed ratio to produce bottles of fruit drink for sale.

   (a)

   A fruit drink is made by mixing mango juice and water in the ratio $3:5$. If 240 ml of mango juice is used, calculate the amount of water needed.

   [2 marks]

   (b)

   Calculate the total volume of fruit drink produced, and express the volume of mango juice as a fraction of the total volume in its simplest form.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Three business partners share their company's annual profit in a fixed ratio, and want to understand how changing the ratio affects their individual shares.

   (a)

   A sum of 4160 dollars is shared between three business partners, Aisha, Ben and Chen, in the ratio $5:3:1$. Calculate how much money each partner receives.

   [3 marks]

   (b)

   The following year the partners agree to change the ratio to $4:3:2$ while keeping the total profit at 4160 dollars. Calculate the new amount each partner receives, and state which partner's share decreased compared to part (a).

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A builder is mixing concrete using a fixed ratio of cement, sand and gravel, and needs to scale the recipe to different total masses while checking material costs.

   (a)

   A concrete mix uses cement, sand and gravel in the ratio $1:2:4$. A builder needs to make 490 kg of concrete mix in total. Calculate the mass of cement required.

   [4 marks]

   (b)

   The builder needs the sand-to-gravel ratio to remain $2:4$ (i.e. $1:2$) but wants exactly 350 kg of sand. Recalculate the required mass of gravel, and the new total mass of the whole concrete mix (cement, sand and gravel), keeping cement at $1$ part relative to the sand as in the original ratio $1:2:4$.

   [4 marks]

   (c)

   Cement costs 0.80 dollars per kg, sand costs 0.30 dollars per kg and gravel costs 0.20 dollars per kg. Using the masses found in part (b) (175 kg cement, 350 kg sand, 700 kg gravel), calculate the total cost of the concrete mix, and express the cost of cement as a percentage of the total cost, to 1 decimal place.

   [5 marks]

   Total for question 4: 13 marks

End of questions