Percentage increase and decrease test worksheet with questions on ordering values, calculating new values, and solving real-world problems.

Let's solve each question step by step with full workings and explanations.

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1. List these quantities in ascending order:

We need to convert all values to the same form (preferably decimals) for easy comparison.

#### a. $ \frac{2}{5},\ 20\%,\ \frac{1}{3},\ 35\% $

Convert each:
- $ \frac{2}{5} = 0.4 $
- $ 20\% = 0.20 $
- $ \frac{1}{3} \approx 0.333 $
- $ 35\% = 0.35 $

Now list in ascending order:
$$
0.20,\ 0.333,\ 0.35,\ 0.4
$$

So:
$$
20\%,\ \frac{1}{3},\ 35\%,\ \frac{2}{5}
$$

✔ Answer: $ 20\%,\ \frac{1}{3},\ 35\%,\ \frac{2}{5} $

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#### b. $ \frac{4}{9},\ 50\%,\ \frac{9}{20},\ 43\% $

Convert:
- $ \frac{4}{9} \approx 0.444 $
- $ 50\% = 0.50 $
- $ \frac{9}{20} = 0.45 $
- $ 43\% = 0.43 $

Order:
$$
0.43,\ 0.444,\ 0.45,\ 0.50
$$

So:
$$
43\%,\ \frac{4}{9},\ \frac{9}{20},\ 50\%
$$

✔ Answer: $ 43\%,\ \frac{4}{9},\ \frac{9}{20},\ 50\% $

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#### c. $ \frac{5}{7},\ 71\%,\ \frac{2}{3},\ 65\% $

Convert:
- $ \frac{5}{7} \approx 0.714 $
- $ 71\% = 0.71 $
- $ \frac{2}{3} \approx 0.666 $
- $ 65\% = 0.65 $

Order:
$$
0.65,\ 0.666,\ 0.71,\ 0.714
$$

So:
$$
65\%,\ \frac{2}{3},\ 71\%,\ \frac{5}{7}
$$

✔ Answer: $ 65\%,\ \frac{2}{3},\ 71\%,\ \frac{5}{7} $

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2. Find the new values:

Use formula:
- Increase: $ \text{New value} = \text{Original} \times (1 + \frac{\%}{100}) $
- Decrease: $ \text{New value} = \text{Original} \times (1 - \frac{\%}{100}) $

#### a. Increase 650 kg by 15%

$$
650 \times (1 + 0.15) = 650 \times 1.15 = 747.5\ \text{kg}
$$

✔ Answer: $ 747.5\ \text{kg} $

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#### b. Increase 48 minutes by 25%

$$
48 \times (1 + 0.25) = 48 \times 1.25 = 60\ \text{minutes}
$$

✔ Answer: $ 60\ \text{minutes} $

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#### c. Decrease 45 by 9%

$$
45 \times (1 - 0.09) = 45 \times 0.91 = 40.95
$$

✔ Answer: $ 40.95 $

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#### d. Increase 300 cm by 90%

$$
300 \times (1 + 0.90) = 300 \times 1.90 = 570\ \text{cm}
$$

✔ Answer: $ 570\ \text{cm} $

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

VAT = 20% of £600
$$
\text{VAT} = 600 \times 0.20 = £120
$$
Total bill = £600 + £120 = £720

Alternatively:
$$
600 \times 1.20 = £720
$$

✔ Answer: £720

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

Deposit = 35% of £375
$$
375 \times 0.35 = £131.25
$$

Remaining = £375 - £131.25 = £243.75

Alternatively:
You pay 65% of the cost (since 100% - 35% = 65%)
$$
375 \times 0.65 = £243.75
$$

✔ Answer: £243.75

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

Discount = 10% of £9.50
$$
9.50 \times 0.10 = £0.95
$$

New price = £9.50 - £0.95 = £8.55

Alternatively:
$$
9.50 \times (1 - 0.10) = 9.50 \times 0.90 = £8.55
$$

✔ Answer: £8.55

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✔ Final Answers Summary:

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

#### 2.
a. $ 747.5\ \text{kg} $
b. $ 60\ \text{minutes} $
c. $ 40.95 $
d. $ 570\ \text{cm} $

#### 3. £720
#### 4. £243.75
#### 5. £8.55

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✔ Total Marks: 20 (All questions answered correctly with working)

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