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Measure this work in **worker-days**: one worker-day means the work done by one worker in one day.","highlights":[{"text":"the same wall","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=original}{\\color{@sky}{12\\times5}}"},{"latex":"\\htmlData{anchor=work}{\\color{@green}{60\\text{ worker-days}}}"}],"highlights":[{"color":"sky","anchor":"original"},{"color":"green","style":"text-color-with-background","anchor":"work"}],"connections":[{"to":"work","from":"original","color":"green","label":"calculate total work"}]},"order":1,"title":"Find total worker-days","description":"Multiply the original number of workers by the original number of days. This earns the method mark, M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=division}{\\color{@amber}{60\\div15}}"},{"latex":"\\htmlData{anchor=days}{\\color{@green}{4\\text{ days}}}"}],"highlights":[{"color":"amber","anchor":"division"},{"color":"green","style":"text-color-with-background","anchor":"days"}],"connections":[{"to":"days","from":"division","color":"green","label":"divide by workers"}]},"order":2,"title":"Share between workers","description":"With the larger workforce, divide the fixed amount of work by the number of workers. The correct calculation and result earn A1."},{"type":"text","order":3,"title":"Check the direction","content":"There are more workers, so the job should take fewer days. The answer is therefore sensible: it would take $4$ days.","highlights":[{"text":"15 workers","location":"specification"}]}]}],"generatedAt":"2026-07-19T07:33:47.457Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":{"methods":[{"id":"afdb4bd9-0024-49ba-9993-7da617995a7e:total_work","label":"Total Work Approach","steps":[{"type":"text","order":0,"title":"Understand the total work","content":"To solve this problem using the **Total Work Approach**, we first find the total size of the job. We measure this in **worker-days**, which represents the total effort needed if one worker did the entire job alone.","highlights":[{"text":"12 workers 5 days","location":"specification"}]},{"type":"text","order":1,"title":"Calculate total worker-days","content":"We calculate the total work by multiplying the number of workers by the number of days:\n\n$$\\text{Total Work} = 12 \\text{ workers} \\times 5 \\text{ days} = 60 \\text{ worker-days}$$\n\nCalculating this correctly earns you the first mark (**M1**)."},{"type":"text","order":2,"title":"Divide by new workers","content":"We now share this total workload of $60$ worker-days among the $15$ workers. To find the number of days it will take them, we divide the total work by the new number of workers:\n\n$$\\text{Days} = \\frac{60 \\text{ worker-days}}{15 \\text{ workers}} = 4 \\text{ days}$$\n\nThis gives us our final answer of **4 days**, earning you the second mark (**A1**).","highlights":[{"text":"15 workers","location":"specification"}]}]},{"id":"afdb4bd9-0024-49ba-9993-7da617995a7e:inverse_proportion_formula","label":"Inverse Proportion Equation","steps":[{"type":"text","order":0,"title":"Understand the inverse relationship","content":"This is an **inverse proportion** problem because as the number of workers increases, the time taken to build the wall decreases.\n\nWhen two quantities are inversely proportional, their product is constant. We can represent this relationship using the inverse proportion equation:\n\n$$W_1 \\times D_1 = W_2 \\times D_2$$\n\nWhere:\n* $W_1$ and $D_1$ are the initial number of workers and days.\n* $W_2$ and $D_2$ are the new number of workers and days.","highlights":[{"text":"It takes 12 workers 5 days to build a wall.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=W1}{\\color{@sky}{12}} \\text{ workers} \\times \\htmlData{anchor=D1}{\\color{@amber}{5}} \\text{ days} = \\htmlData{anchor=W2}{\\color{@purple}{15}} \\text{ workers} \\times \\htmlData{anchor=D2}{\\color{@teal}{x}} \\text{ days}$"},{"latex":"$$$12 \\times 5 = 15 \\times x$$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"W1"},{"color":"amber","style":"text-color","anchor":"D1"},{"color":"purple","style":"text-color","anchor":"W2"},{"color":"teal","style":"text-color","anchor":"D2"}],"connections":[{"to":"W2","from":"W1","color":"sky","label":"Workers increase","style":"dashed"}]},"order":1,"title":"Set up the equation","description":"We substitute the known values into our equation, letting $x$ be the unknown number of days."},{"type":"text","order":2,"title":"Simplify and solve for x","content":"First, calculate the left side of the equation (the total work in 'man-days'):\n\n$$12 \\times 5 = 60$$\n\nNow, substitute this back to solve for $x$:\n\n$$\\begin{aligned} 60 &= 15 \\times x \\\\ x &= \\frac{60}{15} \\\\ x &= 4 \\end{aligned}$$\n\nThis means it will take **4 days** for 15 workers to build the wall.","highlights":[{"text":"Work out how many days it would take 15 workers to build the same wall.","location":"specification"}]}]},{"id":"afdb4bd9-0024-49ba-9993-7da617995a7e:scaling_factor","label":"Scaling Factor Method","steps":[{"type":"text","order":0,"title":"Identify the relationship","content":"The number of workers and the time taken to build the wall are in **inverse proportion**.\n\nThis means that if we increase the number of workers, the time taken to build the wall will decrease by the same proportion (or scale factor).","highlights":[{"text":"12 workers 5 days","location":"specification"},{"text":"15 workers","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$$\\text{Original workers} = \\htmlData{anchor=orig-workers}{\\color{@sky}{12}}$$"},{"latex":"$$$\\text{New workers} = \\htmlData{anchor=new-workers}{\\color{@pink}{15}}$$"},{"latex":"$$$\\text{Scale Factor} = \\frac{\\htmlData{anchor=new-sub}{\\color{@pink}{15}}}{\\htmlData{anchor=orig-sub}{\\color{@sky}{12}}} = \\htmlData{anchor=sf-val}{\\color{@purple}{1.25}}$$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"orig-workers"},{"color":"pink","style":"text-color","anchor":"new-workers"},{"color":"purple","style":"text-color","anchor":"sf-val"}],"connections":[{"to":"orig-sub","from":"orig-workers","color":"sky","label":null,"style":"solid"},{"to":"new-sub","from":"new-workers","color":"pink","label":null,"style":"solid"}]},"order":1,"title":"Calculate the scale factor","description":"First, find the scale factor by which the number of workers increases. We divide the new number of workers by the original number of workers."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$$\\text{Original days} = \\htmlData{anchor=orig-days}{\\color{@amber}{5}}$$"},{"latex":"$$$\\text{Scale Factor} = \\htmlData{anchor=sf-ref}{\\color{@purple}{1.25}}$$"},{"latex":"$$$\\text{New days} = \\frac{\\htmlData{anchor=days-sub}{\\color{@amber}{5}}}{\\htmlData{anchor=sf-sub}{\\color{@purple}{1.25}}} = \\htmlData{anchor=ans-val}{\\color{@green}{4}}$$"}],"highlights":[{"color":"amber","style":"text-color","anchor":"orig-days"},{"color":"purple","style":"text-color","anchor":"sf-ref"},{"color":"green","style":"text-color","anchor":"ans-val"}],"connections":[{"to":"days-sub","from":"orig-days","color":"amber","label":null,"style":"solid"},{"to":"sf-sub","from":"sf-ref","color":"purple","label":null,"style":"solid"}]},"order":2,"title":"Adjust the time","description":"Since the relationship is inversely proportional, multiplying the workers by $1.25$ means we must divide the number of days by $1.25$."},{"type":"text","order":3,"title":"State final answer","content":"It will take 15 workers **4 days** to build the same wall."}]}],"generatedAt":"2026-06-13T01:39:34.033Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":{"percent":88},"walkthroughVideo":{"url":"https://assets.mathsgenie.co.uk/walkthroughs/videos/ac7a77ed-4975-405a-a4f9-3ec8a4872dba.mp4","durationSeconds":77,"posterUrl":"https://assets.mathsgenie.co.uk/walkthroughs/videos/ac7a77ed-4975-405a-a4f9-3ec8a4872dba.jpg"}},{"id":"ae40d109-7527-4556-be8d-bfeb1bcecdf0","revisionId":"31f08a64-1c31-4b03-9d4d-384b113e30f8","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":"hard","totalMarks":2,"sourceTitle":null,"calculatorUse":"non_calc","isCalculation":true,"parts":[{"id":"f8fb8e53-5e0a-4be8-af83-0090b08b1d3e","label":"a","content":"A typist types 1200 words in 15 minutes.\n\nWork out how many minutes it would take the typist to type 2000 words.","markscheme":"- Finds the typing speed per minute: $1200 \\div 15 = 80$ words per minute M1\n- Calculates time for 2000 words: $2000 \\div 80 = 25$ minutes A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Evidence of finding the words per minute rate (e.g., $1200 \\div 15$ or $2000/80$).","code":"M"},{"id":"p2","marks":1,"description":"Correct final answer of 25 minutes.","code":"A","acceptable":["25","25 minutes"]}],"finalAnswers":["25"],"generatedAt":"2026-05-06T14:05:50.629Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"unit_rate","label":"Find the unit rate","steps":[{"type":"text","order":0,"title":"Find one minute","content":"First find the **unit rate**, meaning the number of words typed in one minute. Divide the number of words by the number of minutes:\n\n$$1200 \\div 15 = 80$$\n\nThe typist types $80$ words per minute. This earns **M1** for using the correct method."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$2000 \\div 80 = \\htmlData{anchor=time}{t}$"},{"latex":"$$\\htmlData{anchor=result}{t=25\\text{ minutes}}$"}],"connections":[{"to":"result","from":"time","color":"green","label":"calculate"}]},"order":1,"title":"Find the time","description":"Now divide the required number of words by the typing speed. This earns A1 for calculating 2000 ÷ 80 = 25 minutes."}]}],"generatedAt":"2026-07-20T10:49:04.226Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":{"methods":[{"id":"f8fb8e53-5e0a-4be8-af83-0090b08b1d3e:unitary_words_per_minute","label":"Unitary Method (Rate per Minute)","steps":[{"type":"text","order":0,"title":"Calculate the typing speed","content":"To find out how many words the typist can type in one minute, we divide the total number of words by the time taken.\n\n$$\\text{Typing speed} = \\frac{1200 \\text{ words}}{15 \\text{ minutes}}$$\n\n$$\\text{Typing speed} = 80 \\text{ words per minute}$$","highlights":[{"text":"types 1200 words in 15 minutes","location":"specification"}]},{"type":"text","order":1,"title":"Find the total time","content":"Now, we divide the target word count of $2000$ words by the typing speed of $80$ words per minute to calculate the total time required.\n\n$$\\text{Time taken} = \\frac{2000 \\text{ words}}{80 \\text{ words per minute}}$$\n\n$$\\text{Time taken} = 25 \\text{ minutes}$$","highlights":[{"text":"type 2000 words","location":"specification"}]}]},{"id":"f8fb8e53-5e0a-4be8-af83-0090b08b1d3e:scaling_ratio","label":"Scaling Factor Approach","steps":[{"type":"text","order":0,"title":"Identify the key information","content":"We are given the following information about the typist:\n\n* **Original number of words:** $1200\\text{ words}$\n* **Original time taken:** $15\\text{ minutes}$\n* **Target number of words:** $2000\\text{ words}$\n\nOur goal is to find how many minutes it will take to type the target of $2000$ words using the **scaling factor approach**.","highlights":[{"text":"A typist types 1200 words in 15 minutes.","location":"specification"},{"text":"Work out how many minutes it would take the typist to type 2000 words.","location":"specification"}]},{"type":"text","order":1,"title":"Calculate the scale factor","content":"First, we determine how many times larger the target word count is compared to the original word count. This is called the **scale factor** ($k$).\n\n$$\\text{Scale Factor } (k) = \\frac{\\text{Target words}}{\\text{Original words}}$$\n\nSubstitute the values into the formula:\n\n$$k = \\frac{2000}{1200}$$\n\nSimplify the fraction by dividing the numerator and denominator by $400$:\n\n$$k = \\frac{5}{3}$$"},{"type":"text","order":2,"title":"Apply the scale factor","content":"Since the number of words increases by a scale factor of $\\frac{5}{3}$, the time required will also increase by the same scale factor:\n\n$$\\text{New Time} = \\text{Original Time} \\times k$$\n\nMultiply the original time ($15\\text{ minutes}$) by our scale factor:\n\n$$\\text{New Time} = 15 \\times \\frac{5}{3}$$\n\nTo calculate this easily, divide $15$ by $3$ first, and then multiply by $5$:\n\n$$\\text{New Time} = 5 \\times 5 = 25\\text{ minutes}$$"},{"type":"text","order":3,"title":"Final answer","content":"It would take the typist **25 minutes** to type 2000 words."}]},{"id":"f8fb8e53-5e0a-4be8-af83-0090b08b1d3e:cross_multiplication","label":"Direct Proportion Equation","steps":[{"type":"text","order":0,"title":"Define the variables","content":"Let's define our unknown value. Let $x$ be the number of minutes it takes to type 2000 words.\n\nSince the typing rate is constant, the number of words typed is directly proportional to the time spent typing. This means the ratio of words to minutes remains constant:\n\n$$\\frac{\\text{Words}_1}{\\text{Minutes}_1} = \\frac{\\text{Words}_2}{\\text{Minutes}_2}$$"},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{Case 1: } \\htmlData{anchor=w1}{\\color{@sky}{1200}} \\text{ words in } \\htmlData{anchor=t1}{\\color{@amber}{15}} \\text{ minutes}$"},{"latex":"$$\\text{Case 2: } \\htmlData{anchor=w2}{\\color{@purple}{2000}} \\text{ words in } \\htmlData{anchor=t2}{\\color{@teal}{x}} \\text{ minutes}$"},{"latex":"$$$\\frac{\\htmlData{anchor=ratio1-top}{\\color{@sky}{1200}}}{\\htmlData{anchor=ratio1-bot}{\\color{@amber}{15}}} = \\frac{\\htmlData{anchor=ratio2-top}{\\color{@purple}{2000}}}{\\htmlData{anchor=ratio2-bot}{\\color{@teal}{x}}}$$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"w1"},{"color":"amber","style":"text-color","anchor":"t1"},{"color":"purple","style":"text-color","anchor":"w2"},{"color":"teal","style":"text-color","anchor":"t2"}],"connections":[{"to":"ratio1-top","from":"w1","color":"sky","label":"words","style":"solid"},{"to":"ratio1-bot","from":"t1","color":"amber","label":"minutes","style":"solid"},{"to":"ratio2-top","from":"w2","color":"purple","label":"words","style":"solid"},{"to":"ratio2-bot","from":"t2","color":"teal","label":"minutes","style":"solid"}]},"order":1,"title":"Set up the proportion","description":"We substitute the given values from the question into our proportion equation."},{"type":"text","order":2,"title":"Cross-multiply and solve","content":"To solve for $x$, we cross-multiply to eliminate the fractions:\n\n$$\\begin{aligned} 1200 \\times x &= 2000 \\times 15 \\\\[10pt] 1200x &= 30000 \\end{aligned}$$\n\nNow, divide both sides by $1200$ to isolate $x$:\n\n$$\\begin{aligned} x &= \\frac{30000}{1200} \\\\[10pt] x &= 25 \\end{aligned}$$\n\nIt takes **$25$ minutes** to type 2000 words.","calculator":[{"gdc":{"expression":"30000 / 1200","instructions":"Type 30000 / 1200 and press ENTER."},"ti84":{"expression":"30000 / 1200","instructions":"Type 30000 / 1200 and press ENTER."},"desmos":{"expression":"30000 / 1200","instructions":"Type 30000 / 1200 in the input box."},"description":"Use a calculator to easily verify the division."}]}]}],"generatedAt":"2026-06-13T01:33:36.515Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":{"percent":82},"walkthroughVideo":{"url":"https://assets.mathsgenie.co.uk/walkthroughs/videos/ae40d109-7527-4556-be8d-bfeb1bcecdf0.mp4","durationSeconds":66,"posterUrl":"https://assets.mathsgenie.co.uk/walkthroughs/videos/ae40d109-7527-4556-be8d-bfeb1bcecdf0.jpg"}},{"id":"92312ec1-825a-4d92-bd2e-e109587e7dbd","revisionId":"8d63c4c7-fb96-4c56-b5ad-02ca4d1de00a","questionNumber":"8","questionType":"LA","specification":"","difficulty":2,"difficultyBand":"hard","totalMarks":2,"sourceTitle":"Direct and Inverse Proportion","calculatorUse":"non_calc","isCalculation":true,"parts":[{"id":"2f54cb12-2e5c-406b-86bf-22840bafe044","label":"0","content":"It takes 5 machines 6 hours to produce 1000 DVDs\n\nWork out how long it would take 4 machines to produce 1000 DVDs.","markscheme":"- Calculates total machine hours: $5 \\times 6 = 30$ M1\n- Divides by 4: $30 \\div 4 = 7.5$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Calculates the total machine-hours required (30).","code":"M"},{"id":"p2","marks":1,"description":"Final answer of 7.5.","code":"A"}],"finalAnswers":["7.5"],"generatedAt":"2026-05-06T11:05:41.067Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":{"methods":[{"id":"2f54cb12-2e5c-406b-86bf-22840bafe044:machine_hours","label":"Using Machine-Hours","steps":[{"type":"text","order":0,"title":"Calculate total machine-hours","content":"First, let's find the total amount of work required to produce the $1000$ DVDs. We measure this in **machine-hours**, which represents the total running time needed if only one machine were doing the work.\n\nSince $5$ machines run for $6$ hours, we multiply the number of machines by the number of hours:\n\n$$\\text{Total Machine-Hours} = 5 \\times 6 = 30\\text{ hours}$$","highlights":[{"text":"5 machines","location":"specification"},{"text":"6 hours","location":"specification"}]},{"type":"text","order":1,"title":"Divide by new machines","content":"Now, we want to find how long it takes $4$ machines to do the exact same amount of work ($30$ machine-hours).\n\nWe divide the total machine-hours by the new number of machines:\n\n$$\\text{Time} = \\frac{30\\text{ machine-hours}}{4\\text{ machines}} = 7.5\\text{ hours}$$","highlights":[{"text":"4 machines","location":"specification"}]},{"type":"text","order":2,"title":"State the final answer","content":"It would take $4$ machines **$7.5$ hours** (or $7$ hours and $30$ minutes) to produce the $1000$ DVDs."}]},{"id":"2f54cb12-2e5c-406b-86bf-22840bafe044:scaling_factor","label":"Using Scaling Factors","steps":[{"type":"text","order":0,"title":"Identify the key information","content":"We need to find the time it takes for 4 machines to produce 1000 DVDs, given that:\n\n* **Original number of machines:** $5$\n* **Original time:** $6$ hours\n* **Target number of machines:** $4$\n\nNotice that the quantity of DVDs (1000) remains constant, so we only need to look at how changing the number of machines affects the time.","highlights":[{"text":"5 machines","location":"specification"},{"text":"6 hours","location":"specification"},{"text":"4 machines","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\text{Ratio of machines} = \\frac{\\htmlData{anchor=new-machines}{\\color{@sky}{4}}}{\\htmlData{anchor=orig-machines}{\\color{@amber}{5}}}"},{"latex":"\\text{Time scale factor (reciprocal)} = \\frac{\\htmlData{anchor=recip-top}{\\color{@amber}{5}}}{\\htmlData{anchor=recip-bot}{\\color{@sky}{4}}}"}],"highlights":[{"color":"sky","style":"text-color","anchor":"new-machines"},{"color":"amber","style":"text-color","anchor":"orig-machines"},{"color":"amber","style":"text-color","anchor":"recip-top"},{"color":"sky","style":"text-color","anchor":"recip-bot"}],"connections":[{"to":"recip-bot","from":"new-machines","color":"sky","label":"reciprocal","style":"solid"},{"to":"recip-top","from":"orig-machines","color":"amber","label":"reciprocal","style":"solid"}]},"order":1,"title":"Calculate the scale factor","description":"The number of machines changes from $5$ to $4$. Since fewer machines will take more time, this is an inverse relationship. We find the ratio of change in the number of machines, then take its reciprocal to get our scaling factor for time."},{"type":"text","order":2,"title":"Scale the original time","content":"Now we multiply the original time ($6$ hours) by our reciprocal scaling factor:\n\n$$\\text{New Time} = 6 \\times \\frac{5}{4}$$\n\n$$\\text{New Time} = \\frac{30}{4} = 7.5\\text{ hours}$$"},{"type":"text","order":3,"title":"State the final answer","content":"It will take **$7.5$ hours** (or $7$ hours and $30$ minutes) for 4 machines to produce the 1000 DVDs.\n\n* **Method Mark (M1):** Awarded for showing the calculation $5 \\times 6 = 30$ machine-hours (which is equivalent to multiplying by the scale factor: $6 \\times \\frac{5}{4} = \\frac{30}{4}$).\n* **Accuracy Mark (A1):** Awarded for the correct final answer of $7.5$."}]},{"id":"2f54cb12-2e5c-406b-86bf-22840bafe044:inverse_proportion","label":"Using Inverse Proportion Equation","steps":[{"type":"text","order":0,"title":"Set up the equation","content":"Since the number of DVDs produced (1000 DVDs) remains constant, the time it takes to complete the job is **inversely proportional** to the number of machines working.\n\nLet $t$ be the time in hours and $M$ be the number of machines.\n\nWe can write this relationship as:\n$$t = \\frac{k}{M}$$\n\nwhere $k$ is the constant of proportionality.","highlights":[{"text":"It takes 5 machines 6 hours to produce 1000 DVDs","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=t-val}{\\color{@sky}{6}} = \\frac{k}{\\htmlData{anchor=M-val}{\\color{@amber}{5}}}$"},{"latex":"$$\\htmlData{anchor=k-eq}{k} = \\htmlData{anchor=t-sub}{\\color{@sky}{6}} \\times \\htmlData{anchor=M-sub}{\\color{@amber}{5}} = 30$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"t-val"},{"color":"amber","style":"text-color","anchor":"M-val"}],"connections":[{"to":"t-sub","from":"t-val","color":"sky","label":null,"style":"solid"},{"to":"M-sub","from":"M-val","color":"amber","label":null,"style":"solid"}]},"order":1,"title":"Find the constant","description":"We substitute the known values ($M = 5$ and $t = 6$) into our equation to solve for $k$. This $k = 30$ represents the total machine-hours required to finish the job."},{"type":"text","order":2,"title":"Solve for new time","content":"Now we have our complete formula:\n$$t = \\frac{30}{M}$$\n\nTo find the time it takes for $4$ machines ($M = 4$):\n\n$$\\begin{aligned} t &= \\frac{30}{4} \\\\ t &= 7.5 \\text{ hours} \\end{aligned}$$\n\nTherefore, it will take $7.5$ hours (or 7 hours and 30 minutes) for 4 machines to produce the DVDs.","highlights":[{"text":"Work out how long it would take 4 machines to produce 1000 DVDs.","location":"specification"}]}]}],"generatedAt":"2026-06-12T23:03:07.685Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":{"percent":95},"walkthroughVideo":{"url":"https://assets.mathsgenie.co.uk/walkthroughs/videos/92312ec1-825a-4d92-bd2e-e109587e7dbd.mp4","durationSeconds":69,"posterUrl":"https://assets.mathsgenie.co.uk/walkthroughs/videos/92312ec1-825a-4d92-bd2e-e109587e7dbd.jpg"}}],"subjectCode":"gcse_maths__aqa","summaries":[{"id":"8f0008a5-3ac6-4daa-ab98-050efff8c8c8","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"2efa34ad-c4e1-4fb2-99c7-e40e22697f46","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"6334644e-dba1-4be7-b3e0-97b7a6fc7377","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"71c255df-ec36-40dc-a20c-787ef9075fa1","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"a4bda0dc-d8a6-4b15-bfe5-c086660f9be8","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"b08c8c9b-351b-4fbe-a354-99f17519cfb7","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"b2a500a8-943b-4475-bdba-acc34e9cbfec","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"b4bd99ed-85f3-499c-806e-e8605d933975","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"bb00807a-a770-4cd5-a9a3-4f7f1fae43d5","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"c8d3cd6a-a050-4279-b1c8-092a2e0831ba","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"cc641143-4555-4183-9360-09a0b92261e8","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"d2aac61c-aaaa-4b70-b87a-2b4ead388c73","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"dcd403ca-e74e-4712-be67-2420d24b535b","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"62593c20-a6cd-4a9d-b44e-91ff8dcfe767","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"182f75f6-f7cf-4350-b93a-923288d6b828","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"2118d5a1-2797-4c94-94ed-de149bd9311d","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"316cae9e-40e9-4ab8-9f61-be628b25354f","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":false},{"id":"3a4a646e-1d18-4987-8c4a-2532b3136883","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"3dea0308-e49d-4726-9111-5e36ecdf40ed","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"55f524a9-359f-4c43-987b-043a18fb86b5","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"673dfdcd-9896-4a4e-a3c5-915dc304449b","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"704f2fe1-bf7d-4d5c-a1f4-751ef6502ba3","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"b52d2ac2-2a2c-4a79-96a8-3b8d64b91913","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"bdeb869d-75a4-49dd-8e82-7368d5a1e68a","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"c3ce6dda-d4a3-4979-8dfe-53b8434404d8","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"f0e45ce5-0e33-4809-9d77-5b9f3307f761","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"ff691b7d-38fb-402c-84df-553e039916b8","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"95284614-40ff-4ac9-97f3-a71a07fedfb2","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"15dd20f3-0925-40c1-b6bc-5580f693d254","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"1d2b9e81-6f4f-471e-a039-e2f9def4a426"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and Inverse Proportion","topicId":"10d067f8-e6d9-45de-8116-a7f0fc44a036","topicSidebar":"$L3a","topicSlug":"grade-5-5-2-direct-and-inverse-proportion","topicTitle":"Direct and Inverse Proportion"}]}],"$L3b","$L3c"]}]

Direct and Inverse Proportion

Question 13

Direct and Inverse Proportion Questions

Direct and Inverse Proportion

Question 13

Direct and Inverse Proportion Questions