Percentage P.

1. The compound interest on $1000 at 10% per annum for 3 years, compounded yearly, equals
the simple interest on another $1000 at r % per annum for the same period of time. Calculate
r to 2 decimal places. (6 marks)83-6

2. The monthly income of a man is increased from $8000 to $9000.

(a) Find the percentage increase.
(b) After the increase, the ratio of his savings to his expenditure is 3 : 7 for each month.
How much does he save each month? (4 marks)89-1

3. A person bought 10 gold coins at $3000 each and later sold them all at $2700 each.
(a) Find the total loss.
(b) Find the percentage loss. (4 marks)90-1

4. A man buys some British pounds (£) with 150 000 Hong Kong dollars (HK$) at the rate
£1 = HK$15.00 and puts it on fixed deposit for 30 days.
The rate of interest is 14.60% per annum.
(a) How much does he buy in British pounds?
(b) Find the amount in British pounds at the end of 30 days.
(Suppose 1 year = 365 days and the interest is calculated at simple interest.)
(c) If he sells the amount in (b) at the rate of £1 = HK$14.50, how much does he get in Hong
Kong dollars? (5 marks)91-3

5. What is the simple interest on $100 for 6 months at 3% p.a.? 93-1a

6. A merchant bought an article for $ x . He put it in his shop for sale at a marked price 70%
higher than its cost. The article was then sold to a customer at a discount of 5%.
(a) What was the percentage gain for the merchant by selling the article?
(b) If the customer paid $2907 for the article, find the value of x . (5 marks)94-6

7. Mr. Cheung bought a flat in 1993 for $2 400 000 . He made a profit of 30% when he sold the
flat to Mr. Lee in 1994.
(a) Find the price of the flat that Mr. Lee paid.
(b) Mr. Lee then sold the flat in 1995 for $3 000 000 . Find his percentage gain or loss.
(4 marks)95-4

8. Bank A offers personal loans at an interest rate of 18% per annum. For each successive month
after the day when the loan is taken, loan interest is calculated and an instalment is paid.
(Give answers correct to 2 decimal places.)
(a) Mr. Chen took a personal loan of $ 50 000 from Bank A and agreed to repay the bank in
monthly instalments of $ 9 000 until the loan is fully repaid (the last instalment may be
less than $ 9 000 ). The outstanding balance of his loan for each of the first three months
is shown in Table 1 below.
(i) Complete Table 1 until the loan is fully repaid.
(ii) Find the amount of his last instalment.
(iii) Calculate the total interest earned by the bank. (5 marks)
Percentage P.2

(b) Mrs. Li also took a personal loan of $ 50 000 from Bank A. She agreed to pay $ 9 000
as the first monthly instalment and increase the amount of each instalment by 20% for
every successive month until the loan is fully repaid. The outstanding balance of her loan
for the first month shown in Table 2. Complete Table 2 until the loan is fully repaid.
(4 marks)
(c) Mr. Cheng wants to buy a $ 50 000 piano for his daughter but he has no savings at hand.
He intends to buy the piano by taking a personal loan of $ 50 000 from Bank A. If he
can only save $ 12 000 from his income every month and uses his savings to repay the
loan, can he afford to use the repayment scheme as described in (b)? Explain your answer.
(3 marks)96-12

Table 1 The outstanding balance of Mr. Chen’s loan for each month
Loan Interest Loan Repaid Outstanding
Month
($) ($) Balance ($)
1 750.00 8 250.00 41 750.00
2 626.25 8 373.75 33 376.25
3 500.64 8 499.36 24 876.89
4
5
6

Table 2 The outstanding balance of Mrs. Li’s loan for each month
Instalment Loan Interest Loan Repaid Outstanding
Month
($) ($) ($) Balance ($)
1 9 000.00 750.00 8 250.00 41 750.00
2
3
4
5

9. Suppose the population of a town grows by 2% each year and its population at the end of 1996
was 300 000 .
(a) Find the population at the end of 1998.
(b) At the end of which year will the population just exceed 330 000 ? (6 marks)97-10

10. The marked price of a toy car is $29 . It is sold at a discount of 20%.
(a) Find the selling price of the toy car.
(b) If the cost of the toy car is $18, find the percentage profit. (4 marks)98-7

11. (a) Solve 10 x 2  9 x  22  0 .

(b) Mr. Tung deposited $ 10 000 in a bank on his 25th birthday and $ 9 000 on his 26th
birthday. The interest was compounded yearly at r % p.a., and the total amount he
received on his 27th birthday was $ 22 000 . Find r . (6 marks)00-10
Percentage P.3

12. The price of a textbook was $80 last year. The price is increased by 20% this year.
(a) Find the new price.
(b) Pete is given a 20% discount when buying the textbook from a bookstore this year.
How much does he pay for this book? (4 marks)01-8

13. The radius of a circle is 8 cm . A new circle is formed by increasing the radius by 10% .
(a) Find the area of the new circle in terms of .
(b) Find the percentage increase in the area of the circle. (4 marks)02-6

14. A handbag costs $400. The marked price of the handbag is 20% above the cost. It is sold at a
25% discount on the marked price.
(a) Find the selling price of the handbag.
(b) Find the percentage profit or percentage loss. (4 marks)03-5

15. A sum of $5000 is deposited at 2% p.a. for 3 years, compounded yearly. Find the interest
correct to the nearest dollar. (3 marks)04-3

16. The cost of a calculator is $160. If the calculator is sold at its marked price, then the
percentage profit is 25%.
(a) Find the marked price of the calculator.
(b) If the calculator is sold at a 10% discount on the marked price, find the percentage profit
or percentage loss. (4 marks)05-6

17. The weight of Tom is 20% more than that of John. It is given that Tom weighs 60kg.
(a) Find the weight of John.
(b) The weight of Susan is 20% less than that of Tom. Are Susan and John of the same
weight? Explain your answer. (4 marks)06-6

18. The marked price of a vase is $400. The vase is sold at a discount of 20% on its marked price.
(a) Find the selling price of the vase.
(b) A profit of $70 is made by selling the vase. Find the percentage profit. (4 marks)07-6

19. There are 625 boys in a school and the number of girls is 28% less than that of boys.
(a) Find the number of girls in the school.
(b) There are 860 local students in the school.
(i) Find the percentage of local students in the school.
(ii) It is given that 80% of the boys are local students. If x % of the girls are also local
students, write down the value of x . (5 marks)08-8

20. In a survey, there are 172 male interviewees. The number of female interviewees is 75% less
than that of male interviewees. Find
(a) the number of female interviewees,
(b) the percentage of female interviewees in the survey. (4 marks)09-7
Percentage P.4

21. Mary has 50 badges. The number of badges owned by Tom is 30% less than that owned by
Mary.
(a) How many badges does Tom have?
(b) If Mary gives a certain number of her badges to Tom, will they have the same number of
badges? Explain your answer. (4 marks)10-7

22. The marked price of a birthday cake is $360. The birthday cake is sold at a discount of 45% on
its marked price.
(a) Find the selling price of the birthday cake.
(b) If the marked price of the birthday cake is 80% above its cost, determine whether there
will be a gain or a loss after selling the birthday cake. Explain your answer. (4 marks)11-7

23. The marked price of a handbag is $560 . It is given that the marked price of the handbag is
40% higher than the cost.
(a) Find the cost of the handbag.
(b) If the handbag is sold at $460 , find the percentage profit. (4 marks)sample-4

24. The cost of a chair is $360. If the chair is sold at a discount of 20% on its marked price, then
the percentage profit is 30%. Find the marked price of the chair. (4 marks)pp-4

25. The daily wage of Ada is 20% higher than that of Billy while the daily wage of Billy is 20%
lower than that of Christine. It is given that the daily wage of Billy is $480.
(a) Find the daily wage of Ada.
(b) Who has the highest daily wage? Explain your answer. (4 marks)12-4

26. The marked price of a toy is $255. The toy is now sold at a discount of 40% on its marked
price.
(a) Find the selling price of the toy.
(b) If the percentage profit is 2%, find the cost of the toy. (4 marks)14-6

27. The cost of a book is $250. The book is now sold and the percentage profit is 20%.
(a) Find the selling price of the book.
(b) If the book is sold at a discount of 25% on its marked price, find the marked price of the
book. (4 marks)15-6

28. In a recreation club, there are 180 members and the number of male members is 40% more
than the number of female members. Find the difference of the number of male members and
the number of female members. (4 marks)16-5

29. The marked price of a vase is 30% above its cost. A loss of $88 is made by selling the vase at a
discount of 40% on its marked price. Find the marked price of the vase. (5 marks)18-7
Percentage P.5

30. A wallet is sold at a discount of 25% on its marked price. The selling price of the wallet is
$690.
(a) Find the marked price of the wallet.
(b) After selling the wallet, the percentage profit is 15%. Find the cost of the wallet.
(4 marks)19-5

31. In a recruitment exercise, the number of male applicants is 28% more than the number of
female applicants. The difference of the number of male applicants and the number of female
applicants is 91. Find the number of male applicants in the recruitment exercise.
(4 marks)20-5

32. The marked price of a shirt is higher than its cost by $80. The shirt is sold at a discount of 10%
on its marked price. After selling the shirt, the percentage profit is 30%. Find the marked price
of the shirt. (4 marks)21-6

33. A fan is sold at a discount of 30% on its marked price. After selling the fan, the profit is $78
and the percentage profit is 26%. Find the marked price of the fan. (4 marks)22-5

Answers:
1. 11.03 2. (a) 12.5% (b) $2700
3. (a) $3000 (b) 10% 4. (a) £10000 (b) £10120 (c) HK$146 740
5. $1.5 6. (a) 61.5% (b) 1800
8. (a)(ii) $7606.20 (iii) $2606.20
7. (a) $3 120 000 (b) 3.85% loss
(c) not enough
9. (a) 312 120 (b) At the end of 2001 10. (a) $23.2 (b) 28.9%
11. (a) –2 or 11
2
(b) 10 12. (a) $96 (b) $76.8

13. (a) 77.44 cm2 (b) 21% 14. (a) $360 (b) percentage loss = 10%
15. $306 16. (a) $200 (b) 12.5%
17. (a) 50kg (b) not the same 18. (a) $320 (b) 28%
19. (a) 450 (b)(i) 80% (ii) 80 20. (a) 43 (b) 20%
21. (a) 35 (b) not 22. (a) $198 (b) lost $2
23. (a) $400 (b) 15% 24. $585
25. (a) $576 (b) Christine 26. (a) $153 (b) $150
27. (a) $300 (b) $400 28. 30
29. $520 30. (a) $920 (b) $600
31. 416 32. $260
33. $540