EXERCISE 1.16 (a) The price of a bicycle excluding 15\% VAT is R15 999. Calculate the price including VAT. (b) If a lounge suite costs R12 998 including 15\% VAT, what is the price excluding VAT? (C) A security company is offering a 15\% discount on a home alarm system costing R2 999. What is the discounted price? (d) A shop selling car tyres has a special offer on a brand of tyres. If one tyre is selling for R900 and the discount is $$ 35 \% $$, what was the original selling price of the tyre? (c) The price of car batteries increased from R1 294,04 to R1 302,56. Calculate the percentage increase in the price. (f) A homeowner paid a property tax of R1 161,37 per month before the start of the COVID 19 pandemic. The municipality dropped this amount to R864,33 per month G901 186 to assist the homeowner financially. What was the percentage decrease in the monthly property tax amount? (g) A stationery shop purchases a carton of copy paper at a cost price of R180 and sells a carton for R259. If the shop offers a $$ 40 \% $$ discount on a carton, would the shop make a profit or loss on the sale? Show your calculations to justify your answer. (h) The rental fees for a tenant are currently R7 200 per month. If there is to be an G901 187 increase of $$ 8 \% $$, what will the tenant now pay per month?

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UpStudy AI · Accepted Answer

Sure, let's tackle each part of **Exercise 1.16** step by step:

---

### **(a) Calculating the Price Including 15% VAT**

- **Given:**
  - **Price excluding VAT:** R15,999
  - **VAT rate:** 15%

- **Calculation:**
  $$
  \text{Price including VAT} = \text{Price excluding VAT} \times (1 + \text{VAT rate})
  $$
  $$
  \text{Price including VAT} = 15,\!999 \times 1.15 = 18,\!398.85
  $$

- **Answer:**  
  The price including VAT is **R18 398,85**.

---

### **(b) Determining the Price Excluding 15% VAT**

- **Given:**
  - **Price including VAT:** R12,998
  - **VAT rate:** 15%

- **Calculation:**
  $$
  \text{Price excluding VAT} = \frac{\text{Price including VAT}}{1 + \text{VAT rate}}
  $$
  $$
  \text{Price excluding VAT} = \frac{12,\!998}{1.15} \approx 11,\!302.61
  $$

- **Answer:**  
  The price excluding VAT is approximately **R11 302,61**.

---

### **(c) Calculating the Discounted Price of a Home Alarm System**

- **Given:**
  - **Original price:** R2,999
  - **Discount rate:** 15%

- **Calculation:**
  $$
  \text{Discount} = 2,\!999 \times 0.15 = 449.85
  $$
  $$
  \text{Discounted Price} = 2,\!999 - 449.85 = 2,\!549.15
  $$

- **Answer:**  
  The discounted price is **R2 549,15**.

---

### **(d) Finding the Original Selling Price Before a 35% Discount**

- **Given:**
  - **Discounted price:** R900
  - **Discount rate:** 35%

- **Assumption:**  
  R900 is the price **after** applying the 35% discount.

- **Calculation:**
  $$
  \text{Original Price} = \frac{\text{Discounted Price}}{1 - \text{Discount rate}} = \frac{900}{0.65} \approx 1,\!384.62
  $$

- **Answer:**  
  The original selling price was approximately **R1 384,62**.

---

### **(e) Percentage Increase in the Price of Car Batteries**

*(Note: There's a labeling inconsistency in the original question. This is addressed as part (e) for clarity.)*

- **Given:**
  - **Old price:** R1,294.04
  - **New price:** R1,302.56

- **Calculation:**
  $$
  \text{Increase} = 1,\!302.56 - 1,\!294.04 = 8.52
  $$
  $$
  \text{Percentage Increase} = \left( \frac{8.52}{1,\!294.04} \right) \times 100 \approx 0.66\%
  $$

- **Answer:**  
  The price increased by approximately **0,66 %**.

---

### **(f) Percentage Decrease in Monthly Property Tax**

- **Given:**
  - **Original tax:** R1,161.37 per month
  - **Reduced tax:** R864.33 per month

- **Calculation:**
  $$
  \text{Decrease} = 1,\!161.37 - 864.33 = 297.04
  $$
  $$
  \text{Percentage Decrease} = \left( \frac{297.04}{1,\!161.37} \right) \times 100 \approx 25.56\%
  $$

- **Answer:**  
  The monthly property tax decreased by approximately **25,56 %**.

---

### **(g) Assessing Profit or Loss After a 40% Discount on a Carton of Copy Paper**

- **Given:**
  - **Cost price:** R180
  - **Selling price:** R259
  - **Discount offered:** 40%

- **Calculation:**
  $$
  \text{Discount Amount} = 259 \times 0.40 = 103.60
  $$
  $$
  \text{Selling Price After Discount} = 259 - 103.60 = 155.40
  $$
  $$
  \text{Profit/Loss} = 155.40 - 180 = -24.60
  $$

- **Analysis:**  
  Since the result is negative (**-R24.60**), the shop incurs a **loss**.

- **Answer:**  
  The shop would make a **loss of R24,60** per carton after the discount.

---

### **(h) Calculating the New Monthly Rent After an 8% Increase**

- **Given:**
  - **Current rent:** R7,200 per month
  - **Increase rate:** 8%

- **Calculation:**
  $$
  \text{Increase Amount} = 7,\!200 \times 0.08 = 576
  $$
  $$
  \text{New Rent} = 7,\!200 + 576 = 7,\!776
  $$

- **Answer:**  
  The new monthly rent will be **R7 776**.

---

Feel free to reach out if you need further clarification on any of these parts!
**Solutions to Exercise 1.16:** **(a)** Price including VAT: R18 398,85 **(b)** Price excluding VAT: R11 302,61 **(c)** Discounted price: R2 549,15 **(d)** Original selling price: R1 384,62 **(e)** Percentage increase: 0,66 % **(f)** Percentage decrease: 25,56 % **(g)** The shop incurs a loss of R24,60 per carton. **(h)** New monthly rent: R7 776

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