Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Priya is paid £58.50 for working 7.5 hours on a Saturday. Work out her rate of pay, in £ per hour.

2.y is directly proportional to x. If the value of x is trebled (multiplied by 3), what happens to the value of y?

3.A furniture designer makes a scale model of a wardrobe using a scale of 1 : 8. The real wardrobe is 2.4 m tall and 1.2 m wide. Work out the perimeter of the front face of the model wardrobe, in centimetres.

4.A garden centre has 90 rose bushes in stock. It receives a delivery that increases its stock of rose bushes by 20%. In the same week it sells 150 lavender bushes. Work out the new number of rose bushes, then write it as a fraction of the number of lavender bushes sold, giving your answer in its simplest form.

5.Two mathematically similar containers have a volume scale factor of 64 (the larger container's volume is 64 times the smaller container's volume). Work out the length scale factor between the two containers.

6.Isla says that the ratio 4:6 is equivalent to the ratio 6:9. Is she correct? Give a reason for your answer.

7.In a fruit drink, cranberry juice and apple juice are mixed in the ratio 3:7. Write the amount of apple juice as a fraction of the amount of cranberry juice, in its simplest form.

8.On a straight-line graph the volume of water, V litres, in a tank is plotted on the vertical axis and the time, t minutes, on the horizontal axis. The line passes through (2, 50) and (6, 130). Work out the gradient of the line and give its units.

9.At an animal shelter, the ratio of cats to dogs is 2:5. There are 18 more dogs than cats. Work out the number of cats.

10.Two cars leave the same point at the same time and travel in opposite directions. One travels at 80 km/h and the other at 60 km/h. Work out how long it takes until the cars are 350 km apart.

11.40% of a number is 12 more than 25% of the same number. Work out the number.

12.A textbook is reduced from £60 to £45. Work out the percentage reduction.

13.A shade of paint is made by mixing blue paint and white paint. To make 5 litres of the shade, 2 litres of blue paint is used and the rest is white paint. Write the ratio of blue paint to white paint in its simplest form.

14.Triangle ABC is mathematically similar to triangle PQR, with AB corresponding to PQ and BC corresponding to QR. AB = 6 cm, BC = 8 cm and PQ = 12 cm. Work out the length of QR.

15.In a recipe the mass of chocolate to the mass of milk is in the ratio 1:4. Amelia uses 200 g of milk. Work out the mass of chocolate she needs.