The answer
(a) 20 scones
(b)(i) 26 scones
(ii) 195 g
O-Level E-Math 2025 Paper 1 Question 2 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 2 of the O-Level E-Math 2025 Paper 1. It tests direct proportion / unitary method, in the Ratio, rate & proportion area. It is worth 4 marks: (a) 1, (b)(i) 2 + (ii) 1. It is a worded / diagram-based question, so open your Ten-Year Series (TYS) or the official paper at this question, then follow our full worked solution below.
(a) 8 scones need 60 g of butter, so each scone needs \(\tfrac{60}{8} = 7.5\) g. With 150 g: \(\dfrac{150}{60} \times 8 = 20\) scones.
(b)(i) Find how many scones each stock allows, then take the smallest (limiting ingredient). - Milk: \(\dfrac{700}{150} \times 8 = 37.3\) scones - Flour: \(\dfrac{900}{275} \times 8 = 26.2\) scones - Butter: \(\dfrac{900}{60} \times 8 = 120\) scones - Sugar: \(\dfrac{900}{30} \times 8 = 240\) scones
Flour runs out first, so the maximum is \(26\) whole scones.
(ii) Butter for 26 scones \(= \dfrac{60}{8} \times 26 = 7.5 \times 26 = 195\) g.
Answer: (a) 20 scones
(b)(i) 26 scones
(ii) 195 g
Same structure, different numbers
Swap the constants, dress a quadratic as a length, hide a derivative inside an integral, and a student sees a brand new problem. The structure underneath is the same, and so is the method. Once a student can name the structure, a whole row of questions that look different start to open the same way.
That is where marks really leak: in choosing the method, not in the algebra that follows. We call it Lock and Key, name the lock, then the key follows.
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Genius Plus Academy · O-Level & IP Mathematics
Our O-Level E-Math tuition trains the same recognise-the-structure method these worked solutions show, taught by a team that has marked these papers for years. It runs within our weekly Secondary Math programme, Sec 1 to 4 and IP.
It is a direct proportion / unitary method question from Ratio, rate & proportion, worth 4 marks: (a) 1, (b)(i) 2 + (ii) 1.
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