Ratio and proportion: Practice Questions

Express \(24\) cm as a fraction of \(60\) cm in its simplest form.

A train travels a distance of \(180\) miles at an average speed of \(60\) mph. How long does the journey take?

A sum of \(£40\) is divided between Amy and Ben in the ratio \(3 : 5\). How much money does Ben receive?

A \(500\) ml bottle of juice costs \(£2.00\). What is the cost per \(100\) ml?

Simplify the ratio \( 12 : 30 \) to its simplest form.

A bag contains only blue and red counters in the ratio \(3:7\).
There are \(42\) red counters in the bag.
How many counters are there in the bag in total?

The ratio of the radii of two spheres is \(3:5\).
The surface area of the smaller sphere is \(72\pi\text{ cm}^2\).
Calculate the surface area of the larger sphere in terms of \(\pi\).

A company's profits increased from \(£125,000\) to \(£142,500\).
Express this increase as a percentage of the original profit.

A recipe for 4 people requires \( 200 \text{ g} \) of flour and \( 150 \text{ ml} \) of milk.

(a) How much flour is needed to make the recipe for 10 people?
(b) Express the ratio of flour to milk in its simplest form.

A metal bar has a mass of \( 4.5 \text{ kg} \) and a volume of \( 500 \text{ cm}^{3} \).

(a) Calculate the density of the metal in \( \text{g/cm}^{3} \).
(b) A larger block of the same metal has a volume of \( 1200 \text{ cm}^{3} \). Use your answer from part (a) to find the mass of this block in kilograms.