Sheet № 230 · Foundation + Higher · AQA · Edexcel · OCR
Ratio Given the Difference –
Ratio questions where you are given the difference between two shares — rather than the total — are a common exam trap in GCSE Maths. Many students automatically add the parts and divide the total by this sum, but that only works when you know the total. When the question gives you the difference, you need a different approach: find the d
§Key definitions
Question:
Ali and Ben share some money in the ratio 5 : 3. Ali receives £40 more than Ben. How much does each person receive?
Answer:
Ali receives £100 and Ben receives £60.
Check:
Blue = 21, Green = 12, Red = 9. Blue - Red = 21 - 9 = 12 ✓
Q1 (Foundation):
Two numbers are in the ratio 4 : 9. The larger number is 30 more than the smaller. Find both numbers.
Q2 (Foundation):
Mia and Jake share sweets in the ratio 3 : 5. Jake gets 14 more sweets than Mia. How many sweets are there in total?
§Formulas to memorise
Difference in parts = Larger part - Smaller part
Value of one part = Actual difference / Difference in parts
Write down the ratio — and identify the two quantities being compared.
Find the difference in parts — by subtracting the smaller ratio number from the larger.
Divide the actual difference — (given in the question) by the difference in parts. This gives the value of one part.
Multiply — each ratio number by the value of one part to find each share.
Check — that the difference between your answers matches the difference given in the question.
Worked example
Ali and Ben share some money in the ratio 5 : 3. Ali receives £40 more than Ben. How much does each person receive?
Working:
⚠ Common mistakes
- ✗Dividing the difference by the total parts instead of the difference in parts. If the ratio is 5 : 3 and the difference is £40, divide by 2 (the difference in parts), not by 8 (the total parts).
- ✗Confusing "difference" with "total." Read the question carefully. "Ali gets £40 more than Ben" gives a difference. "They share £400" gives a total. The method is different for each.
- ✗Getting the subtraction order wrong in three-part ratios. Make sure you subtract the correct pair. If the question says "12 more blue than red," subtract the red part from the blue part.
✦ Exam tips
- →Underline or highlight the word "more," "less" or "difference" in the question so you know which method to use.
- →Always write "difference in parts = ..." as your first line of working. This earns a method mark.
- →After finding each share, verify that the difference matches the value given in the question. This catches arithmetic errors and is good exam practice.
- →Three-part ratio questions may tell you the difference between any two parts (not necessarily the largest and smallest). Read carefully to identify which two are being compared.