Percentages (I) · Ages 12–13
Back to the original value
New ÷ (1 ± rate), not the rate taken back off.
How to do it
Method
New ÷ (1 ± rate), not the rate taken back off
x × 1.2 = 144, x = 144 ÷ 1.2 = 120
Another way
Match the percentages
120% is 144, 1% is 1.2, 100% is 120
In full
It is 144 after a 20% increase: what was it? Let the original be x: x × (1 + 20%) = 144, so x = 144 ÷ 1.2 = 120. Or match percentages: 144 is 120% of the original, so 1% is 144 ÷ 120 = 1.2 and 100% is 120. The usual slip is taking 20% of 144 off 144. That 20% is of the original, not of the new value, so divide; don't subtract. Down 25% to 90: x × 75% = 90, x = 90 ÷ 0.75 = 120. Then check: 120 × 1.2 = 144.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
A number increased by 25% is 75, so the number was 60.
True or false?
Show the answer and working
Answer: True
The original = 75 ÷ 1.25 = 60. Taking 25% of 75 off 75 uses the wrong base.
Example 2
Tsz-ching is 5% taller than last year, 131.25 cm now. How tall was Tsz-ching last year?
Show the answer and working
Answer: 125 cm
Last year's height is the base: x × 1.05 = 131.25, so x = 131.25 ÷ 1.05 = 125.
Example 3
A number decreased by 20% is now 72 less than before. The number now =
Show the answer and working
Answer: 288
72 is 20% of the original: the original = 72 ÷ 20% = 360, and now it is 360 − 72 = 288.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.A number increased by 40% is 224, so the number was 134.4.
True or false?
Answer:
2.A number increased by 40% is 56. What was the number?
- A. 16
- B. 33.6
- C. 78.4
- D. 40
Choose the right answer
Answer:
3.The original x becomes 75% of itself, 195: x × 0.75 = 195, x =
Answer:
4.A number decreased by 10% is 450: 450 is % of the original, so the original = 450 ÷ = .
Fill in each blank
Answer:
5.A number decreased by 30% is 364. The number was
Answer:
All the answers
- 1. False
- 2. D. 40
- 3. 260
- 4. 90, 0.9, 500
- 5. 520
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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