A television costs €380 before VAT at 21% has been added - Leaving Cert Mathematics - Question 1 - 2021

To find the total cost of the laptop including VAT, we start by identifying the increment caused by VAT:

$$ext{Increase due to VAT} = €130.20$$

Now, adding this to the net cost:

$$ext{Total cost including VAT} = ext{Cost without VAT} + ext{Increase due to VAT}$$

If we denote the cost without VAT as X:

$$X + 130.20 = X \times 1.21 \Rightarrow 130.20 = 0.21X$$

From this, we can calculate:

$$X = \frac{130.20}{0.21} = €620.00$$

To determine the amount of VAT in the price of the printer, we need to isolate the VAT component from the total price:

Using the formula for VAT included:

$$ext{VAT} = \frac{ ext{Total Price} \times \text{VAT Rate}}{100 + \text{VAT Rate}}$$

Substituting the values:

$$= \frac{290.40 \times 21}{121} = €50.40$$

The saving of €336 is due to the reduction in VAT on 30 computers. First, we find the saving per computer:

$$ext{Saving per computer} = \frac{336}{30} = €11.20$$

Now, with the previous VAT rate of 23%, we can calculate the price before VAT:

Using the formula:

$$ext{Price before VAT} = \frac{ ext{Price including VAT}}{1 + ext{VAT Rate}} = \frac{X}{1.21}$$

Substituting the values:

$$= \frac{€650}{1.21} = €538.84 ext{ (approximately)}$$