age-change/questions","formulaUrl":null,"initialIndex":42,"initialQuestionWindow":[{"id":"de9bc411-7275-4732-b88f-d02d6ef56cc8","revisionId":"54ede91d-b53a-48f7-a072-76bab45e01ef","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":"calc","parts":[{"id":"cd67ea33-68a5-40d4-b90c-87055fcde2f9","label":"a","content":"Last month, David's monthly rent was £820.\n\nThis month, his rent has increased to £871.\n\nWork out the percentage increase in his monthly rent.\n\nGive your answer to 1 decimal place.","markscheme":"- Calculates the increase: $871 - 820 = 51$ M1\n- Uses the percentage change formula: $\\frac{51}{820} \\times 100$ M1\n- Final answer of 6.2% (to 1 dp) A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Find the difference between the two rent values.","code":"M"},{"id":"p2","marks":1,"description":"Set up the fraction (difference over original) and multiply by 100.","code":"M"},{"id":"p3","marks":1,"description":"Calculate the final percentage to 1 decimal place.","code":"A"}],"finalAnswers":["6.2","6.2%"],"generatedAt":"2026-05-06T13:59:59.076Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"percentage_change","label":"Percentage change formula","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{increase}=\\htmlData{anchor=new_rent}{\\color{@sky}{871}}-\\htmlData{anchor=old_rent}{\\color{@amber}{820}}$"},{"latex":"$$\\text{increase}=\\htmlData{anchor=increase_result}{\\color{@sky}{51}}$"}]},"order":0,"title":"Find the increase","description":"Subtract the old rent from the new rent. This earns the first method mark, M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{percentage increase}=\\dfrac{\\text{increase}}{\\text{original amount}}\\times 100$"},{"latex":"$$\\text{percentage increase}=\\dfrac{\\htmlData{anchor=increase_value}{\\color{@sky}{51}}}{\\htmlData{anchor=starting_rent}{\\color{@amber}{820}}}\\times 100$"}]},"order":1,"title":"Set up percentage change","description":"Percentage increase is measured relative to the starting value. Here, the original amount is last month's rent, £820. Substituting into the percentage-change formula earns the second method mark, M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{percentage increase}=\\color{@sky}{\\htmlData{anchor=unrounded}{6.219512\\ldots\\%}}$"},{"latex":"$$\\text{percentage increase}=\\color{@green}{\\htmlData{anchor=rounded}{6.2\\%}}$"}],"connections":[{"to":"rounded","from":"unrounded","color":"green","label":"round to 1 dp"}]},"order":2,"title":"Calculate and round","description":"Calculate the percentage, then round to one decimal place as requested. The second decimal digit is 1, so the first decimal digit stays unchanged. This correct rounded answer earns A1."}]}],"generatedAt":"2026-07-19T02:02:45.375Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"e73c5f90-17ba-49a0-9c01-199651b8e2c3","revisionId":"68f2b079-643b-4ad2-9f12-b995aa1de31b","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":"non_calc","parts":[{"id":"fd73c1a0-b78c-4566-a56e-d39adebedc42","label":"a","content":"David buys a collection of rare stamps for £8 400\nHe sells the collection for £7 392\n\nCalculate the percentage loss David makes.","markscheme":"- Calculates the loss: $8400 - 7392 = 1008$ M1\n- Uses the percentage change formula: $\\frac{1008}{8400} \\times 100$ M1\n- Final answer of 12% A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Finds the difference between the two prices.","code":"M"},{"id":"p2","marks":1,"description":"Calculates the loss as a fraction of the original purchase price.","code":"M"},{"id":"

Percentage Change

Question 36

Percentage Change Questions

Percentage Change

Question 36

Percentage Change Questions