Edexcel IGCSE Math A Higher 1.6 Percentages Questions

Use percentage questions to calculate parts, increases, decreases, original values and compound changes in money or measurement contexts.

Exam points

Calculate percentages of amounts and express one number as a percentage of another.
Use multipliers for percentage increase, decrease, reverse percentages and comparisons.
Apply repeated percentage change to compound interest, depreciation or yearly changes.

Covered syllabus points

1.6.A Meaning of percentage 1.6.B Express a given number as a percentage of another number 1.6.C Express a percentage as a fraction and as a decimal 1.6.D Percentages as operators 1.6.E Simple percentage problems 1.6.F Reverse percentages 1.6.G Compound interest and depreciation 1.6.HA Repeated percentage change 1.6.HB Compound interest problems

[Maximum number: 6]

Gladys buys a table for $ 465 to sell in her shop.
She sells the table for $ 520

(a)

Work out the percentage profit that Gladys makes from the sale of the table. Give your answer correct to 3 significant figures.

Gladys has a sale in her shop.
She decreases all the normal prices by 12%
The normal price of an armchair was $ 550

[ 3 ]

520-465=55 $\frac{55}{465}\times100=11.827956\ldots$

Final answer:
$11.8\%$

A1 for 11.8 or better.

(b)

Work out the sale price of the armchair.
$

[ 3 ]

$0.12\times550=66$ 550-66=484

Final answer:
484

Alternative method:
$0.88\times550=484$

[Maximum number: 3]

Carlos, Flavia and Tazia shared £ 861 between themselves.
The amount of money Flavia got is 65% of the amount of money Carlos got.
The amount of money Tazia got is 22% more than the amount of money Carlos got.
Work out how much money Carlos got.

Let Carlos receive C.

C+0.65C+1.22C=2.87C

2.87C=861

C=\frac{861}{2.87}=300

Final answer:

£300

M1 for 1+0.65+1.22=2.87, or 100+65+122=287.
M1 for $861\div2.87$ , or $(861\div287)\times100$ oe.
A1.
Note: $861\div3=287$ is M0.

[Maximum number: 6]

Chengbo sold a house for 180000 yuan.
The amount for which he sold the house is 24% more than the amount he paid for the house.

(a)

Work out how much Chengbo paid for the house.

Give your answer correct to 3 significant figures.
yuan

Zhi bought a house on 1st January 2017
When she bought the house, its value was 120000 yuan.
The value of the house increased by 1.8\% per year.

[ 3 ]

Original price multiplier:
$100\%+24\%=124\%=1.24$ $180000\div1.24=145161.29\ldots$
Final answer:
145000
Accept 145000 to 145200.

(b)

Work out the value of Zhi's house on 1st January 2020

Give your answer correct to 3 significant figures.
yuan

[ 3 ]

Three years of increase:
$120000\times1.018^{3}=126597.34\ldots$
Final answer:
127000
Accept 126597 to 126600, or 127000 to 3 significant figures.

[Maximum number: 3]

Gladys buys a table for $ 465 to sell in her shop.
She sells the table for $ 520

520-465=55 $\frac{55}{465}\times100=11.827956\ldots$

Final answer:
$11.8\%$

A1 for 11.8 or better.

[Maximum number: 3]

Gladys buys a table for $ 465 to sell in her shop.
She sells the table for $ 520

Work out the sale price of the armchair.
$

$0.12\times550=66$ 550-66=484

Final answer:
484

Alternative method:
$0.88\times550=484$

[Maximum number: 3]

Chengbo sold a house for 180000 yuan.
The amount for which he sold the house is 24% more than the amount he paid for the house.

Original price multiplier:
$100\%+24\%=124\%=1.24$ $180000\div1.24=145161.29\ldots$
Final answer:
145000
Accept 145000 to 145200.

[Maximum number: 3]

Chengbo sold a house for 180000 yuan.
The amount for which he sold the house is 24% more than the amount he paid for the house.

Work out the value of Zhi's house on 1st January 2020

Give your answer correct to 3 significant figures.
yuan

Three years of increase:
$120000\times1.018^{3}=126597.34\ldots$
Final answer:
127000
Accept 126597 to 126600, or 127000 to 3 significant figures.

[Maximum number: 3]

Asha bought an apartment.
The table gives information about the value of apartments, in euros, and the annual service charge band.

Table for Question 8 — Edexcel IGCSE Math A Higher

In 2021, the value of Asha's apartment was 634400 euros.
The value of Asha's apartment had increased by 4% from its value in 2020

Pam bought a boat.
In each year after Pam bought the boat, the value of the boat depreciated by $15\%$ .

Work out the total percentage by which the value of the boat had depreciated by the end of the second year after Pam bought the boat.

After two years, multiplier:
$0.85^2=0.7225$
Depreciation:
1-0.7225=0.2775
Final answer:
$27.75\%$
Accept $27.8\%$ or $28\%$ .

[Maximum number: 3]

Himari invests 200000 yen for 3 years in a savings account paying compound interest.
The rate of interest is 1.8% for the first year and x % for each of the second year and the third year.

The value of the investment at the end of the third year is 209754 yen.
Work out the value of x
Give your answer correct to one decimal place.

$200000\times1.018=203600$ $\sqrt{\frac{209754}{203600}}=1.015000\ldots$ x=1.5

Final answer:
1.5

Accept $1.500045971\ldots$ or better.

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Covered syllabus points

Question 1

Question (a)

Question (b)

Question 2

Question 3

Question (a)

Question (b)

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9