Sec. 4 Percentages

Question 1

a) How do you find x% of y?
e. g.

Answer 1

a) -Turn the % into a decimal/fraction.
- Multiply by 100

Question 2

a) How do you find the new amount after a % inc./dec.
b) a toaster is £38 exc. VAT. VAT is charged at 20%. What is the cost inc. VAT?

Answer 2

a) Find the multiplier that represents the %
e. g. 5% inc. = 1+0.05= 1.05

26% dec.= 1-0.26=0.74

Question 3

a) How do you express x as a % of y?
b) There are 480 pupils in a school. 55% of them are girls and 59 of them have blond hair. What % of the girs have blond hair?

Answer 3

a) -Divide x by y
- Multiply by 100

Question 4

a) How do you find the % change?
b) How is a % change question worded?

Answer 4

a) Use the formula: % change= (diff/OG)x100
b) They will ask you to find % inc./profit or error or dec./ loss or discount

Question 5

a) %Q: How do you find the original value?
e. g. A house dec. in price by 10.55 to £132 600. Find what it was worth before the rise.

Answer 5

Question 6

a) How do you solve a simple interest question?
b) R invests £380 in an account which pays 3% simple interest per year. How much will she have in 4 years?

Answer 6

a)

• Find the interest made in one year ( Find multiplier and x by the amount)
• Multiply this by the no. of years

Question 7

Working with %s questions

Answer 7

Question 8

Working with %s questions

Answer 8

Question 9

a) What is the formula for compound interest?

Answer 9

Question 10

Answer 10

Question 11

Susan buys a car for £6500

a) The car depreciates by 9% each year. How much will it be worth in 3 years?
b) How many complete years will it be before the car is worth less then £3000?

Answer 11

a) Use the formula: 6500(0.91)³

Question 12

Answer 12

Question 13

a) There are 360people in a village. The population has grown by 20% in the last year.

If the population continue sto grow at the same rate, how many years will it be before it doubles in size?

Answer 13

a) Compound interest Q: 360x2=720

1st yr: 1.2x360=432

2nd yr: 1.2x432=518.4

3rd yr: 1.2x 518.4=622.08

4th yr: 1.2x622.08x1.2=746.50

Question 14

A shop keeper sells a pair of gloves for £3.70 and makes a 48% profit.

a) What is thecost price of a pair of socks/
b) The shop has a sale and has a 36% loss on socks. What is the price of the socks during the sale.

Answer 14

£3.70 = 1.48 (148%)

(/1.48)

£2.50 = 100%

? : Why not 1% rather than 100%

Question 15

The owners of a museum are expecting a 14% inc. in visitors next year.

This year they had 20400 visitors.

How many should they expect next year>

Answer 15

1.14 x 20400 =23265

to 3sf + 23300

Method 2

20400x0.14= 2856

20400+2856=23265

Question 16

I wish to invest $5000 for three years and have decided to go with the HR building society.

The Silver account pays 895% interest simple interest per annum.

The Gold account pays 2/.3% simple interest on the first £4000, but no additional money is invested.

How much will I earn if I choose:

a) the silver account
b) the gold account

Answer 16

a) silver:

Type in calc. 5000x1.895% =94.75 (amount per year0

x3=£283.25

without calc. 0.01895x5000=94.75

b) gold:

£4000x2.3%=92

x3= £276

Question 17

Emma makes wooden funiture. It costs her £10 for the materials to make one chair and £7 a day to rent the workshop.

If Emma makes 4 chairs in 5 days and sells them for £120, in total wha is her profit?

Answer 17

Materials =4 x £10=£40 40 +35=75

Rent: 5x£7 = £35 120-75=45

Profit as a % of the money made:

profit/how much cost her 45/75=60%

Question 18

Rob withdraws £340 from his bank account to pay for a telescope, making his account £242 in debit.

He then sells his telescope and deposits his takings back into his account , after which it is £176.20 in credit.

Assuming no other transactions took place during this what was Rob’s % profit on the telescope.

Answer 18

242+176.20= 418.20 - amount he put back into his account

418.20-340=78.20

Profit as a percentage of all the money made (% profit):

78.20/340=0.23

=23%

Question 19

There are appromimately 6000 fish and chip shoops in the UK.

On average a fish and chip shop gets around 160 customers a day.

Given the population of the of the UK is around 60 million, approximately waht % of the population visit a fish and chip shop each day?

Answer 19

(no. of visits per day) 160 x 6000 ( no. of shops)

÷

60x10⁶ (population)

x100 = 1.6%

Question 20

Amy has 20 pets. 60% of are dogs and three of the dogs have black fur.

Without using a calculator, calc. the % of Amy’s dogs that have blac fur.

Answer 20

Calc no. of dogs: 20x0.6 =0.75

3/12 x 100= 25%

Question 21

At a film festival there are 40 movie stars. Daniel meets 85% of them and 16 other people.

What % of the people Daniel met were’nt move stars?

Answer 21

Calc. the no. of movie stars

0.85x40=34

Total no of people: 34=16=50

(16/50)/100=32%