Percentage increase and decrease test | KS3 maths | Teachit - Free Printable

Problem: Percentage Increase and Decrease Test

Below is a detailed solution to each question in the provided test. Let's solve them step by step.

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Question 1: List these quantities in ascending order

#### Part (a):
Quantities: \( \frac{2}{5}, 20\%, \frac{1}{3}, 35\% \)

1. Convert all quantities to decimals for easy comparison:
- \( \frac{2}{5} = 0.4 \)
- \( 20\% = 0.2 \)
- \( \frac{1}{3} \approx 0.333 \)
- \( 35\% = 0.35 \)

2. Arrange in ascending order:
- \( 0.2, 0.333, 0.35, 0.4 \)

3. Convert back to original forms:
- \( 20\%, \frac{1}{3}, 35\%, \frac{2}{5} \)

Answer:
\[ \boxed{20\%, \frac{1}{3}, 35\%, \frac{2}{5}} \]

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#### Part (b):
Quantities: \( \frac{4}{9}, 50\%, \frac{9}{20}, 43\% \)

1. Convert all quantities to decimals:
- \( \frac{4}{9} \approx 0.444 \)
- \( 50\% = 0.5 \)
- \( \frac{9}{20} = 0.45 \)
- \( 43\% = 0.43 \)

2. Arrange in ascending order:
- \( 0.43, 0.444, 0.45, 0.5 \)

3. Convert back to original forms:
- \( 43\%, \frac{4}{9}, \frac{9}{20}, 50\% \)

Answer:
\[ \boxed{43\%, \frac{4}{9}, \frac{9}{20}, 50\%} \]

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#### Part (c):
Quantities: \( \frac{5}{7}, 71\%, \frac{2}{3}, 65\% \)

1. Convert all quantities to decimals:
- \( \frac{5}{7} \approx 0.714 \)
- \( 71\% = 0.71 \)
- \( \frac{2}{3} \approx 0.667 \)
- \( 65\% = 0.65 \)

2. Arrange in ascending order:
- \( 0.65, 0.667, 0.71, 0.714 \)

3. Convert back to original forms:
- \( 65\%, \frac{2}{3}, 71\%, \frac{5}{7} \)

Answer:
\[ \boxed{65\%, \frac{2}{3}, 71\%, \frac{5}{7}} \]

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Question 2: Find the new values

#### Part (a): Increase 650 kg by 15%
1. Calculate 15% of 650 kg:
\[
15\% \text{ of } 650 = 0.15 \times 650 = 97.5 \text{ kg}
\]
2. Add this to the original value:
\[
650 + 97.5 = 747.5 \text{ kg}
\]

Answer:
\[ \boxed{747.5 \text{ kg}} \]

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#### Part (b): Increase 48 minutes by 25%
1. Calculate 25% of 48 minutes:
\[
25\% \text{ of } 48 = 0.25 \times 48 = 12 \text{ minutes}
\]
2. Add this to the original value:
\[
48 + 12 = 60 \text{ minutes}
\]

Answer:
\[ \boxed{60 \text{ minutes}} \]

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#### Part (c): Decrease 45 by 9%
1. Calculate 9% of 45:
\[
9\% \text{ of } 45 = 0.09 \times 45 = 4.05
\]
2. Subtract this from the original value:
\[
45 - 4.05 = 40.95
\]

Answer:
\[ \boxed{40.95} \]

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#### Part (d): Increase 300 cm by 90%
1. Calculate 90% of 300 cm:
\[
90\% \text{ of } 300 = 0.9 \times 300 = 270 \text{ cm}
\]
2. Add this to the original value:
\[
300 + 270 = 570 \text{ cm}
\]

Answer:
\[ \boxed{570 \text{ cm}} \]

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Question 3: A new window costs £600 plus VAT (at 20%). How much is the total bill?

1. Calculate 20% of £600:
\[
20\% \text{ of } 600 = 0.2 \times 600 = 120 \text{ £}
\]
2. Add this to the original cost:
\[
600 + 120 = 720 \text{ £}
\]

Answer:
\[ \boxed{720 \text{ £}} \]

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Question 4: A new TV costs £375. You pay a 35% deposit. How much do you still have to pay?

1. Calculate 35% of £375:
\[
35\% \text{ of } 375 = 0.35 \times 375 = 131.25 \text{ £}
\]
2. Subtract the deposit from the original cost:
\[
375 - 131.25 = 243.75 \text{ £}
\]

Answer:
\[ \boxed{243.75 \text{ £}} \]

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Question 5: A top which used to cost £9.50 was in a 10% off sale. How much does the top cost now?

1. Calculate 10% of £9.50:
\[
10\% \text{ of } 9.50 = 0.1 \times 9.50 = 0.95 \text{ £}
\]
2. Subtract this from the original price:
\[
9.50 - 0.95 = 8.55 \text{ £}
\]

Answer:
\[ \boxed{8.55 \text{ £}} \]

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Final Answers:

1. (a) \( \boxed{20\%, \frac{1}{3}, 35\%, \frac{2}{5}} \)
(b) \( \boxed{43\%, \frac{4}{9}, \frac{9}{20}, 50\%} \)
(c) \( \boxed{65\%, \frac{2}{3}, 71\%, \frac{5}{7}} \)

2. (a) \( \boxed{747.5 \text{ kg}} \)
(b) \( \boxed{60 \text{ minutes}} \)
(c) \( \boxed{40.95} \)
(d) \( \boxed{570 \text{ cm}} \)

3. \( \boxed{720 \text{ £}} \)

4. \( \boxed{243.75 \text{ £}} \)

5. \( \boxed{8.55 \text{ £}} \)