:[{"text":"ABC is a straight line.","location":"specification"}]},{"type":"text","order":2,"title":"Find value per part","content":"We are given that the actual length of $BC$ is $100$ metres. Since $BC$ represents $4$ parts of our ratio, we can find the value of $1$ part by dividing:\n\n$$\\text{Value of 1 part} = \\frac{100\\text{ m}}{4} = 25\\text{ m}$$","highlights":[{"text":"BC = 100 metres.","location":"specification"}]},{"type":"text","order":3,"title":"Scale to find AC","content":"Now, we scale this up to find the total length of $AC$, which represents $5$ parts:\n\n$$\\text{Length of } AC = 5 \\times 25\\text{ m} = 125\\text{ m}$$"}]}],"generatedAt":"2026-06-12T19:31:09.978Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":null},{"id":"5f712e57-9167-47a0-a026-ca85050621a6","revisionId":"292081c5-439d-477d-8c0d-f8404f7d4a53","questionNumber":"10","questionType":"LA","specification":"","difficulty":3,"difficultyBand":"medium","totalMarks":4,"sourceTitle":"Ratio","calculatorUse":"non_calc","parts":[{"id":"b4e9ccec-4ced-4369-927b-135a49433a26","label":"0","content":"Bob is going to make some orange paint.\nHe needs to mix red paint, yellow paint and white paint in the ratio 5 : 4 : 1\n\nBob wants to make 750 ml of orange paint.\n\nBob has\n400 ml of red paint\n300 ml of yellow paint\n200 ml of white paint\n\nDoes Bob have enough red paint, yellow paint and white paint to make the orange paint?\nYou must show all your working.","markscheme":"- Calculate value of one part: $750 \\div 10 = 75$ M1\n- Calculate required amounts: Red = $5 \\times 75 = 375$, Yellow = $4 \\times 75 = 300$, White = $1 \\times 75 = 75$ M1\n- Compare required with available: $375 < 400$, $300 = 300$, $75 < 200$ M1\n- Conclusion: Yes, he has enough. A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Divides total volume by total parts ($750 \\div 10$).","code":"M"},{"id":"p2","marks":1,"description":"Calculates the required volume for at least two colors.","code":"M"},{"id":"p3","marks":1,"description":"Compares all three required volumes to the amounts Bob has.","code":"M"},{"id":"p4","marks":1,"description":"Correct conclusion (Yes) based on working.","code":"A"}],"finalAnswers":["Yes"],"generatedAt":"2026-05-06T11:02:29.678Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"ratio_parts","label":"Find one ratio part","steps":[{"type":"text","order":0,"title":"Add the ratio parts","content":"First find the total number of equal ratio parts:\n\n$$5+4+1=10$$\n\nThe orange paint is split into $10$ equal parts altogether.","highlights":[{"text":"5 : 4 : 1","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=rule}{\\text{one part}=\\dfrac{\\text{total volume}}{\\text{total ratio parts}}}$"},{"latex":"$$\\htmlData{anchor=calc}{\\color{@sky}{750\\text{ ml}\\div 10=75\\text{ ml}}}$"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"calc"}],"connections":[{"to":"calc","from":"rule","color":"sky","label":"substitute"}]},"order":1,"title":"Find one part","description":"Divide the total volume by the total number of ratio parts. Substituting 750 ml and 10 parts gives 75 ml. This calculation earns the first method mark; 75 ml is the volume of one ratio part."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{Red required}=5\\times75=\\htmlData{anchor=red_amount}{\\color{@red}{375\\text{ ml}}}$"},{"latex":"$$\\text{Yellow required}=4\\times75=\\htmlData{anchor=yellow_amount}{\\color{@amber}{300\\text{ ml}}}$"},{"latex":"$$\\text{White required}=1\\times75=\\htmlData{anchor=white_amount}{\\color{@sky}{75\\text{ ml}}}$"}],"highlights":[{"color":"red","style":"text-color-with-background","anchor":"red_amount"},{"color":"amber","style":"text-color-with-background","anchor":"yellow_amount"},{"color":"sky","style":"text-color-with-background","anchor":"white_amount"}]},"order":2,"title":"Calculate each amount

Ratio

Question 51

Ratio Questions

Ratio

Question 51

Ratio Questions