Ratio and proportion：練習問題

Simplify the ratio \( 4.5 \text{ kg} : 750 \text{ g} \) to its simplest form.

It takes 5 identical water pumps exactly 9 hours to completely empty a large swimming pool. How many hours would it take for 3 of these same pumps to empty the pool, assuming they work at the same constant rate?

A map has a scale of \( 1 : 5000 \). On the map, a park has an area of \( 4 \text{ cm}^2 \). Calculate the actual area of the park in hectares.
(Note: \( 1 \text{ hectare} = 10,000 \text{ m}^2 \))

In a secondary school, the ratio of teachers to students is \( 2 : 25 \). If there are 750 students currently enrolled, how many teachers are employed at the school?

A recipe for 8 people requires \( 600\text{ g} \) of flour.
How much flour is needed to make the same recipe for 12 people?

A map has a scale of \( 1:5000 \).
The actual distance between two buildings is \( 450 \text{ m} \). Calculate the distance between these two buildings on the map in centimetres.

A map has a scale of \( 1:50000 \). The actual area of a forest is \( 10 \text{ km}^2 \). Calculate the area of the forest shown on the map in square centimetres.

The force of attraction, \( F \), between two objects is inversely proportional to the square of the distance, \( d \), between them.
Calculate the percentage decrease in the force, \( F \), when the distance, \( d \), is increased by \( 25\% \).

A gardener is working on a project in his garden.
(a) He mixes compost and sand in the ratio \( 45:30 \). Write this ratio in its simplest form.
(b) He makes a batch of potting soil with a total mass of \( 56\text{ kg} \). The potting soil is a mixture of compost, sand, and gravel in the ratio \( 3:2:2 \). Calculate the mass of the compost in this batch.
(c) The gardener looks at a plan of his garden. The plan is drawn to a scale of \( 1:50 \). On the plan, the length of the garden is \( 12\text{ cm} \). Calculate the actual length of the garden in metres.

A production line machine produces 180 components every 1.5 hours.
(a) Calculate how many components the machine produces in 5 hours.
(b) The production cost for each component is 4.20 Swiss Francs (CHF). Calculate the total cost to produce components for 8 hours.
(c) Convert the total cost from part (b) into Euros (€) using the exchange rate €1 = 0.95 CHF. Give your answer to the nearest Euro.