Decrease 40 by a ratio of 4:5.

Without using a calculator, find: a) $\sqrt{225}$ b) $\sqrt{0.01}$ c) $\sqrt{0.81}$ d) $\sqrt{\frac{9}{25}}$ e) $\sqrt{5 \frac{4}{9}}$ f) $\sqrt{2 \frac{23}{49}}$

A train travelling at 100 km/h takes 4 hours for a journey. How long would it take a train travelling at 60 km/h?

Decrease 30 by the following ratios: a) 3:4, b) 2:9, c) 7:12, d) 3:16, e) 5:8, f) 9:20.

A cuboid measuring 3 cm by 5 cm by 2 cm is enlarged by a ratio of 2:1, a) What is the volume of: i) the original cuboid? ii) the enlarged cuboid? b) By what ratio has the volume been increased?

A cube of side 4 cm is enlarged by a ratio of 3:1. a) What is the volume of: i) the original cube? ii) the enlarged cube? b) By what ratio has the volume been increased?

Increase 70 by the following ratios: a) 4:3, b) 5:3, c) 8:7, d) 9:4, e) 11:5, f) 17:14 .

A cuboid measuring 3cm by 5cm by 2cm is enlarged by a ratio of 2 : 1.

a What is the volume of:

i the original cuboid?

ii the enlarged cuboid?

b By what ratio has the volume been increased?

Increase 60 by the following ratios: a) 2:3, b) 5:6, c) 7:12, d) 3:5, e) 1:4, f) 13:15.

Increase 100 by the following ratios: a) 8:5, b) 5:2, c) 7:4, d) 11:10, e) 9:4, f) 32:25.

A square of side length 3 cm is enlarged by a ratio of 3:1. a) What is the area of: i) the original square? ii) the enlarged square? b) By what ratio has the area been enlarged?

A swimming pool is filled in 30 hours by two identical pumps. How much quicker would it be filled if five similar pumps were used instead?

The table below represents the relationship between the speed and the time taken for a train to travel between two stations.

$$\begin{matrix} \text{Speed (km/h)} & \text{60} & \text{ } & \text{ } & \text{120} & \text{90} & \text{50} & \text{10}\\ \text{Time (h)} & \text{2} & \text{3} & \text{4} & \text{ } & \text{ } & \text{ } & \text{ }\\ \end{matrix}$$

Copy and complete the table.

A worker in a sugar factory packs 24 cardboard boxes with 15 bags of sugar in each. If he had boxes which held 18 bags of sugar each, how many fewer boxes would be needed?