1.  Tim bought a new car in 1995 for £10,000 in      2000 the car was priced at £12,500.

Calculate the percentage increase in the price of
the car over the five years.

£10,000 + (a% of £10,000) = £12,500

Hence a% of £10,000 = £2,500

Using the formula:

10,000 x a/100 = 2,500
100a = 2,500
a = 2,500/100 = 25%

In all ratio questions first add the numbers in the ratio:
5 + 3 = 8

Now work out 120/8 = 15

The number of Jeans = 15 x 5 (answer above x the no. of jeans in the ratio) = 75.

So, if we have 75 jeans out of 120, as a percentage this is:

75/120 x 100 = 62.5%

3.  A shop has a 3 day sale where each day, prices are reduced by 10% of the price on the previous day. Before the start of the sale a freezer is priced at
£300. On the first day of the sale the price of the freezer is reduced by 10%.

a) How much is the freezer priced at on the first day of the sale?
b) How much is the freezer priced at on the last day of the sale?

On the first day of the sale a video recorder is priced at £200.

c) How much was the video recorder before the sale?

a) On the first day we have:

£300 - (10% of £300)

10% of £300 = 300 x 10/100 = £30

If £30 is the reduction, the price = £300 - £30 = £270

b) You'll need to calculate the price on the second day first, using the same technique as in a) we get £243.

Apply the same technique again and we get £218.70

c) x - (10% of x) = 200

x = 200/0.9 (see earlier answers for explanation)

= £222.22

4.  Bill shares £180 between his two neices Katie and Amelia. The Ratio of Katie's share to Amelia's share is 5:4.

a) How much is Katie given?
b) How much is Amelia given?

Katie then gives 10% of her share to Amelia.

c) What percentage of the £180 does Amelia now have?

Add the numbers = 5 + 4 = 9

Divide this into the total = £180/9 = £20

a) Katie is given 5 £20 = £100

b) Amelia is given 4 x £20 = £80

c) 10% of Katie's share is 0.1 x 100 = £10, if this is given to Amelia then Amelia has £80 + £10 = £90.

£90 as a % of £180 is 50% (anything that's half of something else is 50%, anything that's a quarter is 25% etc. - remembering the relationship between fractions and percentages can avoid you needing to do any calculations - provided you explain to the examiner how you got your answer!)

5. The most expensive bike at the mountain bike shop can be bought for £560 or it can be payed for with a 25% deposit and 10 monthly payments of £42.
 
How much extra do you need to pay in interest if you opt to pay over 10 months?
 
    

25% of £560 is the same as 1/4 of 560 = £140 (see question 4)

10 payments at £42 = £420, hence the total for the bike paying over 10 months = £140 + £420 = £560.

Hence you pay exactly the same price (no interest)!

6. An advertisement for the new multi-media PC says that the computer is only £799.00 (excluding VAT). If VAT is added at the rate of 17.5% of the selling price, how much do you actually have to pay for the computer when VAT is added?

£799 x 0.175 = £139.83 (this is the amount of VAT you pay to the nearest penny)

Total cost = £799 + £139.33 = £938.83

7. After two years the value of a tractor has fallen to £15,000. After each year passes the depreciation (loss in value) of the tractor has been calculated at 10%.

a) What was the value of the tractor after the first year?
b) What was the original cost of the tractor?

a) x - (10% of x) = £15,000

x = £15,000/0.9 = £16,666.67

b) x - (10% of x) = £16,666.67

x = £16,666.67/0.9 = £18,518.52

8. Business is looking good at "e-Systems" so they have decided to increase their workforce by 20% to cover all the new orders coming in. Before recruiting any new employees, 60 people were working at "e-Systems".

a) Assuming the company could recruit all the people they wanted,  how many were then working at "e-Systems"?

b) If the company found that they could only recruit 75% of the people they wanted, how many were then working at "e-Systems"?

20% of 60 = 60 x 0.2 = 12 people

a) 60 + 12= 72 people

b) Here we have 60 + (75% of 12)

= 60 + 3/4 of 12

= 60 + 9

= 69 people