Cambridge International Mathematics

220 Topics in arithmetic (Chapter 10)

8 Frederik left a wet piece of timber, originally 3 : 80 m long,

outside to dry. In the sun it shrank to a length of 3 : 72 m.

What percentage reduction was this?

9 Shelley was originally farming 250 ha of land. However, she

now farms 270 ha. What percentage increase is this?

CHAIN PERCENTAGE PROBLEMS

When two or more percentage changes occur in succession, we have achain percentage.

We can use a multiplier more than once within a problem to change the value of a quantity.

Example 15 Self Tutor

Increase$3500by10%and then decrease the result by14%.

Increasing by10%has a multiplier of110% = 1: 1

Decreasing by14%has a multipler of86% = 0: 86

So, the final amount= $3500£ 1 : 1 £ 0 : 86

= $3311

Example 16 Self Tutor

A 1 : 25 litre soft drink is bought by a deli for$0: 80. The deli owner

adds60%mark up then15%goods tax. What price does the customer

pay (to the nearest 5 cents)?

A60%mark up means we multiply by 160% = 1: 6

A15%goods tax indicates we multiply by a further115% = 1: 15

) cost to customer =$0: 80 £ 1 : 6 £ 1 : 15

=$1: 472

¼$1: 45 fto the nearest 5 centsg

Example 17 Self Tutor

An investment ofU600 000attracts interest rates of 6 :8%, 7 :1%and 6 :9%

over 3 successive years. What is it worth at the end of this period?

A 6 :8%increase uses a multiplier of 106 :8% = 1: 068

A 7 :1%increase uses a multiplier of 107 :1% = 1: 071

A 6 :9%increase uses a multiplier of 106 :9% = 1: 069

) the final value =U600 000£ 1 : 068 £ 1 : 071 £ 1 : 069

=U733 651

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Y:\HAESE\IGCSE01\IG01_10\220IGCSE01_10.CDR Tuesday, 23 September 2008 3:31:17 PM PETER