Download - Percentages Questions and Answers
![Page 1: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/1.jpg)
Percentages Questions and Answers
•Fractions, Decimals and Percentages•Finding Percentages•Percentage Increase/Decrease•Reverse Percentages•You tube playlist LINK
![Page 2: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/2.jpg)
Percentagesfind Increase (1... Decrease (100-
70%
7%
16.5%
23%
5.25%
16%
3%
11%
Find 12% of 500 500 X 0.12Increase 500 by 12% 500 x 1.12Decrease 500 by 12% 500 x 0.88
![Page 3: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/3.jpg)
Percentagesfind Increase (1... Decrease (100-
70% 0.7 1.7 0.3
7% 0.07 1.07 0.93
16.5% 0.165 1.165 .835
23% 0.23 1.23 0.77
5.25% 0.0525 1.0525 0.9475
16% 0.16 1.16 .84
3% 0.03 1.03 0.97
11% .11 1.11 0.89
Find 12% of 500 500 X 0.12Increase 500 by 12% 500 x 1.12Decrease 500 by 12% 500 x 0.88
![Page 4: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/4.jpg)
N5.4 Increasing and decreasing by a percentage
Contents
N5.5 Reverse percentages
N5 Percentages
N5.1 Fractions, decimals and percentages
N5.6 Compound percentages
N5.2 Percentages of quantities
N5.3 Finding a percentage change
![Page 5: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/5.jpg)
Percentage increase
There are two methods to increase an amount by a given percentage.
The value of Frank’s house has gone up by 20% since last year. If the house was worth £150 000 last year how much is it worth now?
Method 1
We can work out 20% of £150 000 and then add this to the original amount.
= 0.2 × £150 000
= £30 000
The amount of the increase = 20% of £150 000
The new value = £150 000 + £30 000
= £180 000
![Page 6: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/6.jpg)
Percentage increase
We can represent the original amount as 100% like this:
100%
When we add on 20%,
20%
we have 120% of the original amount.
Finding 120% of the original amount is equivalent to finding 20% and adding it on.
Method 2
If we don’t need to know the actual value of the increase we can find the result in a single calculation.
![Page 7: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/7.jpg)
Percentage increase
So, to increase £150 000 by 20% we need to find 120% of £150 000.
120% of £150 000 = 1.2 × £150 000
= £180 000
In general, if you start with a given amount (100%) and you increase it by x%, then you will end up with (100 + x)% of the original amount.In general, if you start with a given amount (100%) and you increase it by x%, then you will end up with (100 + x)% of the original amount.
To convert (100 + x)% to a decimal multiplier we have to divide (100 + x) by 100. This is usually done mentally.
![Page 8: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/8.jpg)
Here are some more examples using this method:
Increase £50 by 60%.
160% × £50 = 1.6 × £50
= £80
Increase £24 by 35%
135% × £24 = 1.35 × £24
= £32.40
Percentage increase
Increase £86 by 17.5%.
117.5% × £86 = 1.175 × £86
= £101.05
Increase £300 by 2.5%.
102.5% × £300 = 1.025 × £300
= £307.50
![Page 9: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/9.jpg)
Percentage decrease
There are two methods to decrease an amount by a given percentage.
A CD walkman originally costing £75 is reduced by 30% in a sale. What is the sale price?
Method 1
We can work out 30% of £75 and then subtract this from the original amount.
= 0.3 × £75
= £22.50
30% of £75 The amount taken off =
The sale price = £75 – £22.50
= £52.50
![Page 10: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/10.jpg)
Percentage decrease
100%
When we subtract 30%
30%
we have 70% of the original amount.
70%
Finding 70% of the original amount is equivalent to finding 30% and subtracting it.
We can represent the original amount as 100% like this:
Method 2
We can use this method to find the result of a percentage decrease in a single calculation.
![Page 11: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/11.jpg)
Percentage decrease
So, to decrease £75 by 30% we need to find 70% of £75.
70% of £75 = 0.7 × £75
= £52.50
In general, if you start with a given amount (100%) and you decrease it by x%, then you will end up with (100 – x)% of the original amount.In general, if you start with a given amount (100%) and you decrease it by x%, then you will end up with (100 – x)% of the original amount.
To convert (100 – x)% to a decimal multiplier we have to divide (100 – x) by 100. This is usually done mentally.
![Page 12: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/12.jpg)
Here are some more examples using this method:
Percentage decrease
Decrease £320 by 3.5%.
96.5% × £320 = 0.965 × £320
= £308.80
Decrease £1570 by 95%.
5% × £1570 = 0.05 × £1570
= £78.50
Decrease £65 by 20%.
80% × £65 = 0.8 × £65
= £52
Decrease £56 by 34%
66% × £56 = 0.66 × £56
= £36.96
![Page 13: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/13.jpg)
Percentage increase and decrease
![Page 14: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/14.jpg)
N5.5 Reverse percentages
Contents
N5 Percentages
N5.1 Fractions, decimals and percentages
N5.6 Compound percentages
N5.2 Percentages of quantities
N5.4 Increasing and decreasing by a percentage
N5.3 Finding a percentage change
![Page 15: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/15.jpg)
Reverse percentagesSometimes, we are given the result of a given percentage increase or decrease and we have to find the original amount.
I bought some jeans in a sale. They had 15% off and I only paid £25.50 for them.
What is the original price of the jeans?
We can solve this using inverse operations.
Let p be the original price of the jeans.
p × 0.85 = £25.50 so p = £25.50 ÷ 0.85 = £30
![Page 16: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/16.jpg)
Sometimes, we are given the result of a given percentage increase or decrease and we have to find the original amount.
I bought some jeans in a sale. They had 15% off and I only paid £25.50 for them.
What is the original price of the jeans?
We can show this using a diagram:
Price before discount.
× 0.85%
Price after discount.
÷ 0.85%
Reverse percentages
![Page 17: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/17.jpg)
Reverse percentages
![Page 18: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/18.jpg)
Reverse percentagesWe can also use a unitary method to solve these type of percentage problems. For example,
Christopher’s monthly salary after a 5% pay rise is £1312.50. What was his original salary?
The new salary represents 105% of the original salary.
105% of the original salary = £1312.50
1% of the original salary = £1312.50 ÷ 105
100% of the original salary = £1312.50 ÷ 105 × 100
= £1250
This method has more steps involved but may be easier to remember.
![Page 19: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/19.jpg)
N5.6 Compound percentages
Contents
N5.5 Reverse percentages
N5 Percentages
N5.1 Fractions, decimals and percentages
N5.2 Percentages of quantities
N5.4 Increasing and decreasing by a percentage
N5.3 Finding a percentage change
![Page 20: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/20.jpg)
A jacket is reduced by 20% in a sale.
Compound percentages
Two weeks later the shop reduces the price by a further 10%.
What is the total percentage discount?
When a percentage change is followed by another percentage change do not add the percentages together to find the total percentage change.
The second percentage change is found on a new amount and not on the original amount.
It is not 30%!
![Page 21: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/21.jpg)
Compound percentages
To find a 10% decrease we multiply by 90% or 0.9.
A 20% discount followed by a 10% discount is equivalent to multiplying the original price by 0.8 and then by 0.9.
To find a 20% decrease we multiply by 80% or 0.8.
original price × 0.8 × 0.9 = original price × 0.72
A jacket is reduced by 20% in a sale.
Two weeks later the shop reduces the price by a further 10%.
What is the total percentage discount?
![Page 22: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/22.jpg)
Compound percentages
This is equivalent to a 28% discount.
The sale price is 72% of the original price.
A 20% discount followed by a 10% discount
A 28% discount
A 20% discount followed by a 10% discount
A 28% discount
A jacket is reduced by 20% in a sale.
Two weeks later the shop reduces the price by a further 10%.
What is the total percentage discount?
![Page 23: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/23.jpg)
Compound percentages
After a 20% discount it costs 0.8 × £100 = £80
Suppose the original price of the jacket is £100.
After an other 10% discount it costs 0.9 × £80 = £72
£72 is 72% of £100.
72% of £100 is equivalent to a 28% discount altogether.
A jacket is reduced by 20% in a sale.
Two weeks later the shop reduces the price by a further 10%.
What is the total percentage discount?
![Page 24: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/24.jpg)
Jenna invests in some shares.
Compound percentages
After one week the value goes up by 10%.
The following week they go down by 10%.
Has Jenna made a loss, a gain or is she back to her original investment?
To find a 10% increase we multiply by 110% or 1.1.
To find a 10% decrease we multiply by 90% or 0.9.
original amount × 1.1 × 0.9 = original amount × 0.99
Fiona has 99% of her original investment and has therefore made a 1% loss.
![Page 25: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/25.jpg)
Compound percentages
![Page 26: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/26.jpg)
Jack puts £500 into a savings account with an annual compound interest rate of 6%.
Compound interest
How much will he have in the account at the end of 4 years if he doesn’t add or withdraw any money?
At the end of each year interest is added to the total amount in the account. This means that each year 5% of an ever larger amount is added to the account.
To increase the amount in the account by 5% we need to multiply it by 105% or 1.05.
We can do this for each year that the money is in the account.
![Page 27: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/27.jpg)
At the end of year 1 Jack has £500 × 1.05 = £525
Compound interest
At the end of year 2 Jack has £525 × 1.05 = £551.25
At the end of year 3 Jack has £ 551.25 × 1.05 = £578.81
At the end of year 4 Jack has £578.81 × 1.05 = £607.75
(These amounts are written to the nearest penny.)
We can write this in a single calculation as
£500 × 1.05 × 1.05 × 1.05 × 1.05 = £607.75
Or using index notation as
£500 × 1.054 = £607.75
![Page 28: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/28.jpg)
How much would Jack have after 10 years?
Compound interest
After 10 years the investment would be worth
£500 × 1.0510 = £814.45 (to the nearest 1p)
How long would it take for the money to double?
£500 × 1.0514 = £989.97 (to the nearest 1p)
£500 × 1.0515 = £1039.46 (to the nearest 1p)
Using trial and improvement,
It would take 15 years for the money to double.
![Page 29: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/29.jpg)
Compound interest
![Page 30: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/30.jpg)
We can use powers to help solve many problems involving repeated percentage increase and decrease. For example,
Repeated percentage change
The population of a village increases by 2% each year.If the current population is 2345, what will it be in 5 years?
To increase the population by 2% we multiply it by 1.02.
After 5 years the population will be
2345 × 1.025 = 2589 (to the nearest whole)
What will the population be after 10 years?
After 5 years the population will be
2345 × 1.0210 = 2859 (to the nearest whole)
![Page 31: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/31.jpg)
Repeated percentage change
The car costs £24 000 in 2005. How much will it be worth in 2013?
To decrease the value by 15% we multiply it by 0.85.
After 8 years the value of the car will be
£24 000 × 0.858 = £6540 (to the nearest pound)
The value of a new car depreciates at a rate of 15% a year.
There are 8 years between 2005 and 2013.
![Page 32: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/32.jpg)
Reverse
• Bought a car 1 year ago and it has lost 45% of its value and is worth £ 3000 now, what did it cost me?
• ? X .55 = £3000 so ? = 3000/0.55 = £5454.55
![Page 33: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/33.jpg)
Compound
• Invest £ 5000 for 5 years earns 3% compound interest
• 5000 x 1.03^5
![Page 34: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/34.jpg)
Percentagesfind Increase (1... Decrease (100-
70% 0.7 1.7 0.3
7% 0.07 1.07 0.93
16.5% 0.165 1.165 .835
23% 0.23 1.23 0.77
5.25% 0.0525 1.0525 0.9475
16% 0.16 1.16 .84
3% 0.03 1.03 0.97
11% .11 1.11 0.89
Find 12% of 500 500 X 0.12Increase 500 by 12% 500 x 1.12Decrease 500 by 12% 500 x 0.88
![Page 35: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/35.jpg)
Fractions, Decimals and Percentages
Home
1. a) 75%b) 10%c) 20%d) 35%e) 42%
2. a) 0.7b) 0.25c) 0.3d) 0.15e) 0.05
3. a) 60% b) 70%c) 8%d) 27%e) 80%
4. a) ¼b) 33/100c) 51/100d) 4/5e) 1/5
5. a) 0.4b) 0.9c) 0.74d) 0.03e) 0.05
6. a) 7/10b) 3/5c) 11/50d) 7/20e) 21/50
![Page 36: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/36.jpg)
Finding Percentages
Home
1) Some percentages I can find easily by doing a single sum, what single sums can I do to find:a. 10% b. 50% c.25%
2) If I know 10% how can I find:a. 5% b. 1% c. 20 % d. 90%
3) If I know 50% how can I find:a. 5% b. 25%
4) Find:a. 30% of 250 b. 40% of 500 c. 15% of 220 d. 75% of 84
5) Find:a. 35% of 440 b. 65% of 450 c. 16% of 220 d. 82% of 96
6) Find:a. 94% of 640 b. 8% of 520 c. 27% of 220 d. 53% of 96
7) Compare you methods for the questions above with a partner, where they the same ?
ANSWERS
1.
a) divide by 10b) divide by 2c) divide by 4
2. a) half the answerb) divide by 10c) double d) multiply by 9 or
subtract 10% from original quantity
3. a) divide by 10b) half 50%
4. a) 75b) 200c) 33d) 63
5. a) 154b) 292.5c) 35.2d) 78.72
6. a) 601.6b) 41.6c) 59.4d) 50.88
![Page 37: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/37.jpg)
Percentage Increase/Decrease
Home
1. Explain how you would use a calculator to increase an amount by a given percent.
2. Increase the following amounts by 42%a)£225b) £306c)£125d)£448e)£512
3. A TV costs £120, how much will it cost if its price is increased by:
a) 12%b)31%c)55%d)62.5%e)99.9%
4. Simon puts £70 in a bank, each year the money in his bank increase by 5.5%, how much does he have in:
a) 1 yearb)2 yearsc)5 years?
5. Explain how you would use a calculator to decrease an amount by a given percent.
6. Decrease the following amounts by 28%a) £225b) £306c) £125d) £448e) £512
7. A TV costs £120, how much will it cost if its price is decreased by:
f) 19%g) 32%h) 79%i) 73.5%j) 42%
8. A car bought for £6, 500 depreciates in value by 12.5% each year, how much will it be worth after:
k) 1 yearl) 2 yearsm) 5 years?
ANSWERS1. 2.
a) 319.5b)434.52c)177.5d) 636.16e)727.04
3. a)134.40b)157.20c)186d)195e)239.88
4. a)73.50b) 77.91c)91.49
5. 6.
a)162b)220.32c)90d) 322.56e)368.64
7. a)97.20b) 81.60c)25.20d)31.80e)69.60
8. a)5687.50b) 4976.56c)333.91
![Page 38: Percentages Questions and Answers](https://reader035.vdocument.in/reader035/viewer/2022062408/568130cf550346895d96e7bd/html5/thumbnails/38.jpg)
Reverse Percentages
Home
1. What would you multiply an amount by to increase it by:
a) 15%b)25%c)4%d)0.5%e)13.5%
2. Find the original prices of these prices that have been increased by the given percentage:
a) Cost= £49.5 after 10% increaseb)Cost= £74.75 after 15% increasec)Cost= £61 after 22% increased)Cost= £104 after 30% increasee)Cost= £120 after 50% increase
3. I have £252 in my bank account; this is due to me earning 5% interest on what I originally had put in. How much money did I have originally in my bank account?
4. What would you multiply an amount by to decrease it by:
a) 15%b)25%c)4%d)0.5%e)13.5%
5. Find the original prices of these items that have been decreased by the given percentage:a) Cost= £72 after 10% decreaseb) Cost= £93.5 after 15% decreasec) Cost= £39 after 35% decreased) Cost= £4 9fter 40% decreasee) Cost= £67.50 after 55% decrease6. A Cars value has dropped by 11.5% it is now worth £3053.25, what was it worth when it was new?
Answers1.
a)1.15b)1.25c) 1.04d)1.005e)1.135
2. a)45b)65c) 50d)80e)80
3. 2404.
a)0.85b)0.75c) 0.96d)0.995e)0.865
5. a)80b)110c) 60d)15e)150
6. 3450