Bills, Tax, Currency and Speed

Bills, VAT and value for money

A bill usually has three parts: units used × price per unit, a fixed standing charge, and then VAT added on top.

Total before VAT = (units × price per unit) + standing charge

A shortcut: to add 23% VAT, multiply by $1.23$. To add 13.5% VAT, multiply by $1.135$.

Taking VAT off again

If a price already includes VAT, it is $100\% + 23\% = 123\%$ of the price before VAT. So to get back to the price before VAT, divide by 1.23.

Value for money

To compare two sizes, find the price per unit (for example, per 100 g). The lower price per unit is better value.

Pay, tax and net pay

Gross pay is what you earn before anything is taken off. Net pay is what you take home.

Net pay = gross pay − income tax payable (− other deductions)

Overtime is paid at a higher rate. Time and a half means $1.5 \times$ the hourly rate. Double time means $2 \times$ the hourly rate.

Income tax

In Ireland, income tax has two rates. A standard rate (20%) applies up to the standard rate cut-off point, and a higher rate (40%) applies to the rest. After working out the tax, you subtract tax credits. Credits reduce the tax itself, not the pay.

Currency conversion

An exchange rate tells you how much of one currency you get for €1. With €1 = £0.85:

• euro to pounds: multiply by 0.85

• pounds to euro: divide by 0.85

Time and average speed

Speed, distance and time are linked by one formula and its two rearrangements:

Cover the one you want: D = S × T, S = D ÷ T, T = D ÷ S.

Time must be in hours

If the speed is in km/h, the time must be in hours. Change minutes to a fraction of an hour by dividing by 60.

To find the length of a journey, subtract the clock times. From 09:50 to 12:20: 09:50 to 10:00 is 10 min, 10:00 to 12:00 is 2 h, then 20 min. Total 2 h 30 min.

Average speed for a whole journey

Profit, loss and mark-up

A shop buys goods at the cost price (CP) and sells them at the selling price (SP).

• Profit = SP − CP (if SP is bigger)

• Loss = CP − SP (if CP is bigger)

• Percentage profit $= \dfrac{\text{profit}}{\text{cost price}} \times 100\%$

Percentage profit or loss is always worked out on the cost price.

A sale reduction is a percentage taken off the selling price.

If a price is in euro and a customer pays in sterling, work out the euro price first, then convert it.

Summary

• Bill: units × price per unit + standing charge, then add VAT (multiply by 1.23 for 23%). To remove VAT, divide by 1.23.

• Value for money: compare the price per 100 g, per litre, per unit. Lower is better.

• Gross pay includes overtime. Tax = 20% up to the cut-off, 40% on the rest, then subtract tax credits. Net pay = gross pay − tax payable.

• Currency: euro to foreign, multiply by the rate. Foreign to euro, divide.

• Speed = distance ÷ time, with time in hours. Average speed = total distance ÷ total time, never the mean of two speeds.

• Percentage profit or loss is a percentage of the cost price. A sale reduction is a percentage of the original selling price.

Back to the start: Niamh's extra data cost €31.75 − €22 = €9.75 including VAT. Before VAT it was $9.75 \div 1.23 = \text{€}7.93$, so the VAT was about €1.82. Try the full question below.