ata{anchor=blue-val}{\\color{@sky}{40}} \\text{ litres}$"},{"latex":"$$\\text{Volume of White} = \\frac{3}{8} \\times \\htmlData{anchor=blue-sub}{\\color{@sky}{\\text{Volume of Blue}}}$"},{"latex":"$$\\text{Volume of White} = \\frac{3}{8} \\times \\color{@sky}{40}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"blue-val"},{"color":"sky","style":"text-color","anchor":"blue-sub"}],"connections":[{"to":"blue-sub","from":"blue-val","color":"sky","label":"substitute","style":"solid"}]},"order":1,"title":"Set up the calculation","description":"We substitute the given volume of blue paint into our fractional formula."},{"type":"text","order":2,"title":"Calculate the result","content":"Now we calculate the final volume of white paint:\n\n$$\\text{Volume of White} = \\frac{3}{8} \\times 40$$\n\nFirst, divide $40$ by $8$:\n\n$$40 \\div 8 = 5$$\n\nThen, multiply the result by $3$:\n\n$$3 \\times 5 = 15 \\text{ litres}$$\n\nThis method matches the markscheme directly by finding the value of one part ($40 \\div 8 = 5$ for the first method mark M1), then multiplying by the $3$ parts of white paint to get $15$ litres (M1 A1).","highlights":[{"text":"40 litres","location":"specification"}]}]}],"generatedAt":"2026-06-12T12:26:28.017Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":null},{"id":"3e6c6d67-6ccd-40b2-97eb-7635c907e1a6","revisionId":"dfe50eb4-e08d-4316-abf7-302b33a722f7","questionNumber":null,"questionType":"LA","specification":"$$LMN$ is a straight wooden plank.","difficulty":1,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":"non_calc","parts":[{"id":"303fae15-bda1-4406-b62a-5502c907f0dd","label":"a","content":"The length of $MN$ is five times the length of $LM$.\n\n$LN = 72$ millimetres.\n\nWork out the length of $MN$.","markscheme":"- Identify the ratio $LM : MN$ as $1 : 5$ or state there are $1 + 5 = 6$ parts M1\n- Calculate the value of one part: $72 \\div 6 = 12$ M1\n- Calculate $MN$: $5 \\times 12 = 60$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Identifies the ratio as $1 : 5$ or calculates the total number of parts (6).","code":"M"},{"id":"p2","marks":1,"description":"Divides the total length by the number of parts ($72 \\div 6$).","code":"M"},{"id":"p3","marks":1,"description":"Multiplies the unit part by 5 to find $MN$.","code":"A"}],"finalAnswers":["60"],"generatedAt":"2026-05-06T14:05:45.402Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"ratio_parts","label":"Use ratio parts","steps":[{"type":"text","order":0,"title":"Write the ratio","content":"Since $MN$ is five times as long as $LM$, take $LM$ as one part and $MN$ as five parts:\n\n$$LM:MN=1:5$$\n\nIdentifying this ratio earns the first **M1** mark.","highlights":[{"text":"The length of $MN$ is five times the length of $LM$.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$1+5=\\htmlData{anchor=parts}{\\color{@sky}{6\\text{ parts}}}$"},{"latex":"$$72\\div \\htmlData{anchor=six}{\\color{@sky}{6}}=\\htmlData{anchor=onepart}{\\color{@amber}{12\\text{ mm}}}$"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"parts"},{"color":"sky","style":"text-color-with-background","anchor":"six"},{"color":"amber","style":"text-color-with-background","anchor":"onepart"}]},"order":1,"title":"Find one part","description":"The whole plank LN contains all the parts. Using 6 total parts to calculate 72 ÷ 6 = 12 mm earns the second M1 mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$MN=5\\times \\htmlData{anchor=onepart}{\\color{@green}{12}}$"},{"latex":"$$MN=\\htmlData{anchor=answer}{\\color{@green}{60\\text{ mm}}}$"}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"onepart"},{"color":"green","style":"text-color-with-background","anchor":"answer"}],"connections":[{"to":"answer","from":"onepart","color":"green","label":"multiply

Ratio

Question 34

Ratio Questions

Ratio

Question 34

Ratio Questions