Worksheet on percentage increases and decreases with various word problems.

Problem Analysis and Solution

The provided image contains a series of problems related to percentage increases and decreases. Below, I will solve each problem step by step.

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Problem 1: Percentage Calculations

#### 1a. Find 120% of 75
To find 120% of 75:
\[
120\% = \frac{120}{100} = 1.2
\]
\[
1.2 \times 75 = 90
\]
Answer: \( \boxed{90} \)

#### 1b. Find 135% of 820
To find 135% of 820:
\[
135\% = \frac{135}{100} = 1.35
\]
\[
1.35 \times 820 = 1107
\]
Answer: \( \boxed{1107} \)

#### 1c. Find 85% of 340
To find 85% of 340:
\[
85\% = \frac{85}{100} = 0.85
\]
\[
0.85 \times 340 = 289
\]
Answer: \( \boxed{289} \)

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Problem 2: House Price Increase

A house cost £200,000 in 2006. By 2011, the price had risen by 20%. What is the new cost of the house?

#### Step 1: Calculate the increase in price
\[
20\% \text{ of } £200,000 = \frac{20}{100} \times 200,000 = 0.2 \times 200,000 = £40,000
\]

#### Step 2: Add the increase to the original price
\[
\text{New price} = £200,000 + £40,000 = £240,000
\]

Answer: \( \boxed{£240,000} \)

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Problem 3: Television Sale Discount

A new television costs £600. In a sale, there is a 10% off. What is the new price of the television?

#### Step 1: Calculate the discount amount
\[
10\% \text{ of } £600 = \frac{10}{100} \times 600 = 0.1 \times 600 = £60
\]

#### Step 2: Subtract the discount from the original price
\[
\text{New price} = £600 - £60 = £540
\]

Answer: \( \boxed{£540} \)

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Problem 4: Car Value Depreciation

A new car costs £9495. In the first year, its value drops by 30%. What is it worth at the end of the first year?

#### Step 1: Calculate the depreciation amount
\[
30\% \text{ of } £9495 = \frac{30}{100} \times 9495 = 0.3 \times 9495 = £2848.50
\]

#### Step 2: Subtract the depreciation from the original price
\[
\text{Value after 1 year} = £9495 - £2848.50 = £6646.50
\]

Answer: \( \boxed{£6646.50} \)

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Problem 5: Car Value Depreciation

A different car originally costs £12,500. In the first year, its value drops by 20%. What is it worth at the end of the first year?

#### Step 1: Calculate the depreciation amount
\[
20\% \text{ of } £12,500 = \frac{20}{100} \times 12,500 = 0.2 \times 12,500 = £2,500
\]

#### Step 2: Subtract the depreciation from the original price
\[
\text{Value after 1 year} = £12,500 - £2,500 = £10,000
\]

Answer: \( \boxed{£10,000} \)

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Problem 6: Nurse's Wage Increase

A nurse’s wage increases by 3%. If she was earning £21,540 last year, how much is she earning now?

#### Step 1: Calculate the increase in wage
\[
3\% \text{ of } £21,540 = \frac{3}{100} \times 21,540 = 0.03 \times 21,540 = £646.20
\]

#### Step 2: Add the increase to the original wage
\[
\text{New wage} = £21,540 + £646.20 = £22,186.20
\]

Answer: \( \boxed{£22,186.20} \)

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Problem 7: Office Manager Bonus

An office manager receives a 7% bonus on his wage. If his wage is £35,235, how much is his bonus?

#### Step 1: Calculate the bonus amount
\[
7\% \text{ of } £35,235 = \frac{7}{100} \times 35,235 = 0.07 \times 35,235 = £2,466.45
\]

Answer: \( \boxed{£2,466.45} \)

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Extension Problem: Car Value Depreciation Over Two Years

A car originally cost £15,000. In the first year, its value dropped by 25%. In the second year, its value dropped by another 15%. What is it worth now?

#### Step 1: Calculate the value after the first year
\[
25\% \text{ of } £15,000 = \frac{25}{100} \times 15,000 = 0.25 \times 15,000 = £3,750
\]
\[
\text{Value after 1 year} = £15,000 - £3,750 = £11,250
\]

#### Step 2: Calculate the value after the second year
\[
15\% \text{ of } £11,250 = \frac{15}{100} \times 11,250 = 0.15 \times 11,250 = £1,687.50
\]
\[
\text{Value after 2 years} = £11,250 - £1,687.50 = £9,562.50
\]

Answer: \( \boxed{£9,562.50} \)

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Final Answers

1. \( \boxed{90} \)
2. \( \boxed{1107} \)
3. \( \boxed{289} \)
4. \( \boxed{£240,000} \)
5. \( \boxed{£540} \)
6. \( \boxed{£6646.50} \)
7. \( \boxed{£10,000} \)
8. \( \boxed{£22,186.20} \)
9. \( \boxed{£2,466.45} \)
10. \( \boxed{£9,562.50} \)