Ratio and proportion: Practice Questions

A map is drawn to a scale of 1 : 50,000. If the distance between two towns on the map is \( 8 \text{ cm} \), what is the actual distance between them in kilometers?

The variable \( y \) is inversely proportional to \( x \). When \( x = 4 \), the value of \( y \) is \( 9 \). Determine the value of \( y \) when \( x = 6 \).

The population of a town increases by \( 10\% \) in 2022 and then decreases by \( 10\% \) in 2023. What is the overall percentage change in the population from the start of 2022 to the end of 2023?

A bag contains \( 60 \) sweets. The sweets are shared between three children in the ratio \( 2 : 3 : 5 \).
How many sweets does the child with the largest share receive? <\/p>

In a container, the ratio of red counters to blue counters is \( 3:4 \). The ratio of blue counters to green counters is \( 5:2 \). What is the ratio of red counters to green counters in its simplest form?

A map has a scale of \(1 : 50,000\). If the distance between two towns on the map is \(8.4 \text{ cm}\), calculate the actual distance in kilometres.

The variable \(y\) is inversely proportional to the square of \(x\). Given that \(y = 9\) when \(x = 2\), find the value of \(y\) when \(x = 6\).

The ratio of red beads to blue beads in a jar is \(3 : 4\). The ratio of blue beads to green beads is \(5 : 2\). Calculate the ratio of red beads to green beads in its simplest form.

The volume, \(V\), of a gas is inversely proportional to the pressure, \(P\), exerted on it. When the pressure is \(100 \text{ units}\), the volume is \(500 \text{ units}\).
(a) Find a formula for \(V\) in terms of \(P\).
(b) Calculate the volume when the pressure is increased to \(250 \text{ units}\).
(c) Calculate the pressure required to reduce the volume to \(125 \text{ units}\).