**UCAT** **Question Analysis - Quantitative Reasoning Question 5**

A restaurant owner calailates the amounts he should charge his customers for each dish or bottle (the "menu price') with the following formulae: Menu Price for food = 3 x cost of the ingredients for the dish excluding VAT x (1+ VAT rate)

Menu Price for a bottle of wine = 4 x purchase price of the bottle excluding VAT x (1 VAT rate) where VAT is calculated at a rate of 20%. In addition, a 12% service charge is payable on the whole bill for groups of 6 or above only. Groups of 5 or fewer pay no service charge.

**A couple visit the restaurant and decide to drink tap water only, which comes for free. The meal costs them a total of £158. **

**Q5.1 How much did the ingredients cost for that meal (excluding VAT)? **

a. £41.16

b. £42.13

c. E43.89

d. £44.37

e. £52.67

**The restaurant has bought ingredients for a price excluding VAT of £50. **

**Q5.2 If they used all the ingredients, what price would a party of 6 people pay for the meal in total, excluding any drinks? **

a. £150

b. £165

c. £168

d. £180

e. £201.60

**A couple incurs a total bill of £172, which includes £48 for a bottle of wine. **

**Q5.3 How much is the average cost of ingredients por person (excluding VAT)? **

a. £.16.53

b. £.17.22

c. £.20.64

d. £.34.44

e. £41.28

**A lone customer has a total bill fn which the drinks represent 60% of the total price. The restaurant spent £32 excluding VAT on ingre-dients. **

**Q5.4 What was the total bill? **

a. £115.20

b. £160

c. £192

d. £240

e. £288

**Answer and Explanation**

**Q5.1 — c: £43.89 **

The cost of the ingredients is 158 / 1.2 / 3 = £43.89.

**Q5.2 — e: £201.60 **

The party would pay: 50 x 3 x 1.2 (VAT) x 1.12 (service) = £201.60.

**Q5.3 — b: £17.22**

Without the wine, the total bill for the food is 172 — 48 = £124. The cost of the ingredients per person is therefore: 124 / 1.2 (VAT) / 3 (cost multiplier) / 2 (number of people) = £17.22.

**Q5.4 — e: £288 **

We know that the ingredients cost £32, therefore the price charged to cus-tomers for the food part of the meal will be 32 x 3 x 1.2 = £115.20. Since the drinks account for 60% of the total bill, then the food accounts for 40%. Therefore the total bill is: 115.20 / 0.4 = £288.

Drafted by Juno Wong (UCAT Prep)