Percentages (I) · Ages 12–13
One change after another
Multiply the factors; never add the rates.
How to do it
Method
Multiply the factors; never add the rates
+20% then −20%: 1.2 × 0.8 = 0.96, 4% down
Another way
Start from 100
100 → 120 → 96
In full
In changes one after another, the second rate is taken on the value after the first, so multiply; never add the rates. Up 20% then down 20%: one way, multiply, 1.2 × 0.8 = 0.96, which is 4% down, not back to the start. Another: start from 100 and go step by step, 100 → 120 → 96. Growing 10% a year, two years make 1.1 × 1.1 = 1.21 times, 21% up; losing 20% a year, two years leave 0.8 × 0.8 = 0.64, 64% of the start. Comparing two amounts works alike: 'A is 25% more than B' takes B as the base, A = B × 1.25; 'by what percentage is B less than A' takes A as the base.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
100 goes up 10%, then up 25% more: the result =
Show the answer and working
Answer: 137.5
After the first it is 110; the second takes 110 as its base, not 100: 110 × (1 + 25%) = 137.5.
Example 2
A number goes up 50%, then down 10%. It ends at % of where it started
Show the answer and working
Answer: 135
Multiply: 1.5 × 0.9 = 1.35, that is 135%. Or start from 100 and go step by step.
Example 3
A number goes up 25%, then down 25%, and ends where it started.
True or false?
Show the answer and working
Answer: False
1.25 × 0.75 = 0.9375. Only a result of 1 brings it back to the start.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.A $100 item goes up 50%, then down 50%. How does its price now compare with before?
- A. 50% lower
- B. The same
- C. 25% lower
- D. 25% higher
Choose the right answer
Answer:
2.A number goes up 300%, then down 75%, and ends where it started.
True or false?
Answer:
3.A number goes up 50%, then down 25%. It ends at % of where it started
Answer:
4.Ka-yee has saved 300% more than Ming. By what percentage is Ming's saving less than Ka-yee's?
- A. 25%
- B. 300%
- C. 75%
- D. 400%
Choose the right answer
Answer:
5.A machine worth $28,000 loses 10% of its value each year. What is it worth after two years?
Answer:
All the answers
- 1. C. 25% lower
- 2. True
- 3. 112.5
- 4. C. 75%
- 5. 22,680 dollars
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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