OCR GCSE Mathematics: Ratio: simplifying, dividing, ratios and fractions (J560) – Practice Questions

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs – examination boards hold copyright in their own papers. Use these alongside the official past papers from your board or school.

These questions cover section 5.01, Calculations with ratio, from the OCR GCSE (9-1) Mathematics (J560) specification, Version 2.1 (August 2026), first assessment 2017. All of the content is Foundation and Higher: nothing here is Higher tier only. Read the study guide first if a method is unfamiliar, and use the revision notes to check formulas. Course hub: OCR GCSE Mathematics. Printable checklist.

Questions

1. Equivalent ratios.

(a) Simplify 36 : 84. [1] (b) Simplify 1.5 km : 600 m. [2] (c) Write 20 : 8 in the form 1 : n. [2]

2. Share £720 between three people in the ratio 2 : 3 : 4. [3]

3. The ratio of tulips to daffodils in a garden bed is 4 : 9.

(a) There are 27 daffodils. How many tulips are there? [2] (b) In a second bed with the same ratio there are 20 tulips. How many daffodils are there? [2]

4. Maya and Ravi share some money in the ratio 9 : 4. Maya receives £65 more than Ravi. Work out how much each person receives. [4]

5. In a hall the ratio of adults to children is 7 : 5.

(a) What fraction of the people in the hall are children? [1] (b) There are 180 people in the hall. How many are children? [2]

6. A fruit drink contains 450 ml of orange juice, 0.3 litres of pineapple juice and 750 ml of apple juice. Write the ratio orange : pineapple : apple in its simplest form. [3]

7. A recipe makes 12 flapjacks using 300 g of oats, 200 g of butter and 150 g of syrup.

(a) Work out the amount of each ingredient needed to make 18 flapjacks. [3] (b) Only 500 g of butter is available. What is the greatest number of flapjacks that can be made, if the other ingredients are not limited? [2]

8. Concentrate and water are mixed in the ratio 1 : 7. Let x be the litres of concentrate and y the litres of water.

(a) Write y in terms of x. [1] (b) Find y when x = 2.5. [1] (c) Explain why the graph of y against x passes through the point (0, 0). [1] (d) A hire charge is C = 4t + 10 pounds for t hours. Show that C and t are not always in the same ratio. [2]

9. Sam, Tia and Uma share £1,260. Sam receives 2/7 of the total. The rest is shared between Tia and Uma in the ratio 3 : 2.

(a) Work out how much each person receives. [4] (b) Write the ratio of Sam’s share to Tia’s share to Uma’s share in its simplest form. [2] (c) The same sharing is used for a total of £1,575. How much does Tia receive? [2]

10. A bag holds red and blue counters in the ratio 5 : 3. After 12 more blue counters are put in, the ratio of red to blue is 5 : 6.

(a) Work out how many red and blue counters were in the bag at the start. [5] (b) What fraction of the counters in the bag at the end are blue? [2]

11. Mix A is blue and white paint in the ratio 2 : 3. Mix B is blue and white paint in the ratio 3 : 7. A decorator combines 5 litres of mix A with 20 litres of mix B.

(a) Find the ratio of blue paint to white paint in the combined mixture. Give your answer in its simplest form. [5] (b) What fraction of the combined mixture is blue paint? [2]

Answers

1. (a) HCF of 36 and 84 is 12, so 36 : 84 = 3 : 7 [1] (b) Same unit: 1.5 km = 1500 m, giving 1500 : 600 [1]. Divide by 300 to get 5 : 2 [1] (c) 8 ÷ 20 = 0.4 [1], so the ratio is 1 : 0.4 [1] Examiner insight: Converting both quantities to the same unit is the step that matters in part (b), so write it down. In part (c), n is the second number divided by the first, and a decimal is an acceptable form for n.

2. Total parts 2 + 3 + 4 = 9 [1]. One part is 720 ÷ 9 = 80 [1]. Shares are £160, £240 and £320 [1] (check 160 + 240 + 320 = 720). [3] Examiner insight: State the value of one part clearly. A check that the shares sum to the total is quick and catches most slips.

3. (a) 27 daffodils is 9 parts, so one part is 3 [1]. Tulips: 4 × 3 = 12 [1] (b) 20 tulips is 4 parts, so one part is 5 [1]. Daffodils: 9 × 5 = 45 [1] Examiner insight: Match each given number to the correct side of the ratio. Tulips come first in the ratio, so 20 goes with the 4.

4. The difference is 9 - 4 = 5 parts [1]. 5 parts = £65, so one part is £13 [1]. Maya receives 9 × 13 = £117 [1]. Ravi receives 4 × 13 = £52 [1]. [4] Examiner insight: The £65 is a difference, not a total, so it equals 5 parts rather than 13 parts. Checking that 117 - 52 = 65 confirms the answer.

5. (a) There are 7 + 5 = 12 parts, so children are 5/12 of the people. [1] (b) One part is 180 ÷ 12 = 15 [1]. Children: 5 × 15 = 75 [1] Examiner insight: The denominator is the total number of parts, 12, not 7 or 5. Reading which group the question asks about decides the numerator.

6. 0.3 litres = 300 ml [1]. The ratio is 450 : 300 : 750 and the HCF is 150 [1]. So the ratio is 3 : 2 : 5 [1]. [3] Examiner insight: A unit conversion for pineapple juice is needed before any simplifying. Working in millilitres avoids decimals.

7. (a) Scale factor 18 ÷ 12 = 1.5 [1]. Oats 300 × 1.5 = 450 g, butter 200 × 1.5 = 300 g [1], syrup 150 × 1.5 = 225 g [1]. [3] (b) 500 ÷ 200 = 2.5 batches of 12 [1]. 2.5 × 12 = 30 flapjacks [1]. [2] Examiner insight: A single scale factor applies to every ingredient. In part (b), comparing the butter available with the butter in one batch is a short, clear way to set up the working.

8. (a) For each 1 of concentrate there are 7 of water, so y = 7x [1] (b) y = 7 × 2.5 = 17.5 litres [1] (c) When there is no concentrate (x = 0) there is no water (y = 0), because y is a multiple of x with no added constant. [1] (d) For t = 1, C = 14, and for t = 3, C = 22 [1]. The ratios C : t are 14 : 1 and 22 : 3, which are different, so they are not always in the same ratio [1]. [2] Examiner insight: A “show that” is best answered by choosing two specific values and comparing them in full. A statement that the line has a fixed charge supports the numbers but does not replace them.

9. (a) Sam: 2/7 × 1260 = £360 [1]. The rest is 1260 - 360 = £900 [1]. Tia: 3/5 × 900 = £540 [1]. Uma: 2/5 × 900 = £360 [1]. [4] (b) The ratio is 360 : 540 : 360 [1], which simplifies by 180 to 2 : 3 : 2 [1]. [2] (c) The ratio 2 : 3 : 2 has 7 parts, and 1575 ÷ 7 = 225 [1]. Tia receives 3 × 225 = £675 [1]. [2] Examiner insight: In part (a) the second sharing applies to what is left after Sam’s share, not to the whole £1,260. Part (c) rewards using the simplified ratio from part (b).

10. (a) Let the starting numbers be 5k red and 3k blue [1]. After adding blue counters there are 3k + 12 blue [1]. Red to blue is now 5k : (3k + 12) = 5 : 6, so 3k + 12 = 6k [1]. Then 3k = 12 and k = 4 [1]. At the start there were 20 red and 12 blue counters [1]. [5] (b) At the end there are 20 red and 24 blue, which is 44 counters [1]. The blue fraction is 24/44 = 6/11 [1]. [2] Examiner insight: Set the problem up with a letter for one part and write the changed quantity before forming the new ratio. Checking that 20 : 24 simplifies to 5 : 6 confirms the answer to part (a).

11. (a) Mix A has 5 parts for 5 litres, so blue is 2 litres and white is 3 litres [1]. Mix B has 10 parts for 20 litres, so one part is 2 litres [1]. Blue in B is 3 × 2 = 6 litres and white is 7 × 2 = 14 litres [1]. Totals are blue 2 + 6 = 8 litres [1] and white 3 + 14 = 17 litres, so the ratio is 8 : 17 [1]. [5] (b) The total volume is 25 litres [1]. The blue fraction is 8/25 [1]. [2] Examiner insight: Find the real amount of each colour in each mix before combining. Adding the two ratios directly (2 : 3 and 3 : 7) does not work because the volumes are different.

Where marks are usually lost

• Not converting to the same unit before simplifying, as in questions 1 and 6.
• Dividing by one number from the ratio instead of by the sum of the parts.
• Putting the numbers in the wrong order, so the larger quantity is paired with the smaller ratio number.
• Treating a given difference as a total, as in question 4.
• Using 7 or 5 as the denominator instead of 12 when turning a ratio into a fraction.
• Applying a second sharing to the original total rather than to the remainder.
• Adding a new quantity to a ratio number instead of to the real amount in a changing-ratio problem.
• Adding two ratios together to combine mixtures of different volumes.
• Stopping before the answer is in its simplest form.
• Skipping a quick sum check when shares are found.

Next steps

• Go back to the study guide for the explanations.
• Use the revision notes for the method boxes and self-test.
• Return to the OCR GCSE Mathematics hub or the checklist.
• Take one of the free 10-minute diagnostics to see where to practise next.
• Book a free trial class.

Official syllabus

OCR, GCSE (9-1) Mathematics (J560), specification Version 2.1 (August 2026), first assessment 2017, section 5.01 Calculations with ratio.