AQA GCSE Mathematics Paper 1 (Foundation), June 2025: Question 12

6 marks · Easy difficulty · Multi-step Problem

Calculate the total charge for late trains given a fraction of total trains run, and calculate the number of coffees sold from a three-part ratio and total drinks sold.

Practise this question

Question

Question 12 consists of two parts. Part (a) states that a company runs 240 trains, 1/8 of which are late, with a £350 charge per late train, asking for the total charge. Part (b) states hot drinks are sold in the ratio tea to coffee to hot chocolate of 3 to 5 to 2, with 2600 total drinks sold, asking for how many coffees are sold.

Mark scheme

Show the mark scheme Mark scheme for question 12. For 12(a): M2 for 240 divided by 8 multiplied by 350 (or M1 for correct first step like 240 times 350), A1 for 10 500. For 12(b): M1 for 2600 divided by (3 + 2 + 5) or 260, M1dep for 260 multiplied by 5, A1 for 1300, with special cases noted.

How to answer it

Fractions of Amounts & Sharing in a Ratio

📌 What this question tests

Core Foundation / Higher tier arithmetic & proportional reasoning skills:

  • Fractions of a quantity: Finding a unit fraction of an integer (dividing by the denominator) and applying multi-step context multiplication.
  • Sharing a quantity into a given ratio: Identifying the total number of parts, finding the value of one single part, and scaling up to find a specific category share.
Question 12 (a) • 3 Marks

Calculating Train Delay Charges (Fraction of Amount)

A company runs 240 trains. 1/8 are late. The charge is £350 per late train. How much is the company charged?

📐 Step-by-Step Method

  1. Find the number of late trains:
    Divide the total trains by 8:
    240 ÷ 8 = 30 late trains
  2. Calculate total cost:
    Multiply the number of late trains by the cost per train (£350):
    30 × 350 = £10 500
Alternative valid method:
Calculate cost if all trains were late: 240 × £350 = £84 000 (M1)
Then take 1/8 of total cost: £84 000 ÷ 8 = £10 500 (M2, A1)

✅ Correct Answer

£10 500

Mark Scheme Breakdown:
• M1: Correct first single operator step (e.g. 240 ÷ 8 or 240 × 350 or 84 000 )
• M2: Complete method seen: 240 ÷ 8 × 350 oe
• A1: Correct answer: 10 500

💡 Key Knowledge

  • To find 1/n of any number, divide that number by n.
  • Multiplication with multiples of 10: 30 × 350 can be broken into (3 × 35) × 100 = 105 × 100 = 10 500 .

❌ Common Errors

  • Finding on-time trains instead: Subtracting 30 from 240 to get 210, then multiplying 210 × 350 . Always re-read whether the question asks for late or on-time trains.
  • Place value slips: Writing £1 050 or £105 000 due to miscounting zeros during multiplication.
Question 12 (b) • 3 Marks

Sharing in a Three-Part Ratio (Hot Drinks Sold)

Ratio is tea : coffee : hot chocolate = 3 : 5 : 2. Total drinks sold = 2600. How many coffees are sold?

📐 Step-by-Step Method

  1. Find the total number of parts:
    3 + 5 + 2 = 10 parts
  2. Find value of 1 part:
    Divide total drinks by total parts:
    2600 ÷ 10 = 260 drinks per part
  3. Find number of coffees:
    Coffee has 5 parts in the ratio:
    260 × 5 = 1300 coffees
Shortcut insight:
Since coffee is 5 parts out of a total of 10 parts, coffee is exactly half ( 5/10 = 1/2 ) of the total drinks: 2600 ÷ 2 = 1300 (implies M2 directly).

✅ Correct Answer

1300

Mark Scheme Breakdown:
• M1: 2600 ÷ (3 + 5 + 2) or 260 seen
• M1dep: their 260 × 5 (dependent on 1st M mark)
• A1: 1300
• Special Case (SC2): An answer of 780 (tea), 520 (hot chocolate), or 6500 (assuming 2600 was the smallest share).

🧠 Exam Technique: The Three R's of Ratio

  • Match labels to parts carefully: Write them directly above the numbers:
    T : C : H = 3 : 5 : 2
  • Do not write the final answer as a ratio: Notice the mark scheme explicitly states that leaving the answer as 780 : 1300 : 520 loses the final accuracy mark (A0). The question asked specifically "How many coffees?", so give a single value.

❌ Common Errors

  • Selecting the wrong drink: Calculating 3 parts (780 for tea) or 2 parts (520 for hot chocolate).
  • Dividing by the wrong number: Dividing by 3 because there are three items, rather than summing the ratio parts ( 3 + 5 + 2 = 10 ).
  • Treating 2600 as one category: Calculating 2600 ÷ 2 = 1300 , then multiplying by 5 to get 6500 (thinking 2600 was only hot chocolate).

Topics

Number · Ratio, proportion and rates of change · 3.1.2 Fractions, decimals and percentages · 3.3 Ratio, proportion and rates of change

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 1 (Foundation), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.