Find 1%
A simple method which will work very well for percentage questions is to find
what one percent is, and then multiply to get any other percentage.
1) Find 25% of 280.
1% is 2.80 (move decimal point two places to the left to make the number smaller)
25% is 25 x 2.8 = 70 (This could be done quicker by remembering that 25% is ¼.
2) Find 20% of 600
1% is 6.00
20% is 20 x 6 = 120 (This could be done quicker by remembering that 20% is 1/5.)
3) Find 33% of 45
1% is 0.45
33% is 14.85 (This cannot be done much faster as 33% isn’t exactly 1/3, but is close.)
4) Find 50% of 240
5) Find 25% of 180
6) Find 12.5% of 80
Question: €100 add 50%, you get €150, take away 50% what do you get?....
The great thing about the ‘Find 1%’ idea is that we can use it to take away
percentages which have been added already.
7) A radio costs €78.65 including VAT of 21%, we want to find the price before VAT
was added. This is very useful if you are working in a shop or claiming back VAT if
you’re a contractor.
The radio cost started at 100% and got another 21% of this added on to it, so €78.65 is
actually 121%.
How much is 1%? 78.65/121 = 0.65, so 1% is 65cent hence 100% is 100 x 65c =€65.
8) A bottle champagne costs €90.75 including 21% VAT Find the price before VAT
1% = 90.75 / 121 = 0.75, so the price without VAT was €75
9) A footballer pays tax at 40%.Their take home pay is 60% of their Gross pay. How
much does it cost the club in Gross pay if the football player takes home €9,000 per
week?
9,000 = 60%, so 1% = 9000/60 = 150, so 100% is 150 x 100 = €15,000
10) A bottle of perfume costs €38.72 including VAT of 21%. How much does it cost
before VAT is added?
11) It costs €1,493.14 to buy a plasma TV including 21% VAT. How much was it
before the VAT?
12) A builder charges €517.56 for a small job, which includes VAT at 13.5%. How
much was it before VAT?
13) What is the difference between 33% of €1,000,000 and 1/3 of €1,000,000?
14) Two shops advertise the same computer for a month then they both reduce the
price. Which is the better deal, the shop which pays the 21% VAT for you, or the shop
which takes 18% off the price?
( Hint: Think of a price and try it. Does it make a difference what price we test with? )
Expressing as a Percentage To express 23 as a percentage of 115,
23 / 115 x 100 = 20%, (you can divide and multiply in the same calculation, no need
to stop and write down the 23/115 and type it back into the calculator)
15) 2 as a percentage of 8: 2/8 x 100 = 25%
16) 3 as a percentage of 60 : 3/60 x 100 = 5%
17) 300 as a percentage of 75: 300/75 x 100 = 400%
18) What is 14 as a percentage of 70?
19) What is 56 as a percentage of 70?
20) What is 123 as a percentage of 3075?
21) What is 0.025 as a percentage of 0.1?
22) Is it cheaper to give one euro tax for every seven earned or to pay tax at 14%?
23) An architect always charges 10% of the builder’s bill before the builder adds
VAT. The architect adds 21% VAT and the builder adds 13.5% VAT. Can you tell
how much the architect got from a total bill of €2,512 including VAT from both?
Homework
1) Find 3% of 200.
2) Find 23% of 65.
3) Find 21% of 56 and add it to 56.
4) Increase 600 by 10%
5) Decrease 700 by 20%
6) A restaurant adds 45% to the price of the ingredients to cover running costs, and
then adds 50% to this amount to cover wages. (No vat.)
If the ingredients for a meal cost €4 what does the meal cost?
If the meal cost €26.10 how much were the ingredients?
7) A bicycle hire company believes that a bike will last for 150 hires before it’s worn
out, lost, or stolen. The bike costs €75 before VAT. How much does it need to make
per hire just to cover the cost of the bike? How much does it charge when it adds
21%VAT to this amount?
8) A Canadian tourist spends €3,267 on holiday including VAT of 21%. They claim
back the VAT when they leave Ireland. How much do they get back?
9) 23 of 1840 Germans speak Greek, 29 of 1450 French people speak Greek and 31 of
1550 Russians speak Greek. Which Nationality is best at speaking Greek?
Homework Solutions
1) 6
2) 14.95
3) 67.76
4) 660
5) 560
6) €8.70, €12
7) 50c, 60 ½ c
8) €567
9) Joint French Russian
Homework Solutions
1) 6
2) 14.95
3) 67.76
4) 660
5) 560
6) €8.70, €12
7) 50c, 60 ½ c
8) €567
9) Joint French Russian
Homework Solutions
1) 6
2) 14.95
3) 67.76
4) 660
5) 560
6) €8.70, €12
7) 50c, 60 ½ c
8) €567
9) Joint French Russian
Solutions for ‘Find 1%’ page 1
4) 120
5) 45
6) 10
Question
The point of the Question is that if you take 50% of 150 away from 150 you get 75.
So after adding 50% and taking 50% away we end up with less than we started with!
This is possible since we added 50% of 100 but took away 50% of 150. If we had
added 50% of 100 and taken away 50% of 100 we would have ended up with 100. So
be careful if someone reduces your wages by 5% and then increases the wages by 5%.
10) €32
11) €1,234
12) €456
13)€3,333.33
14) Imagine the computer costs €500. If it had 100% in it before VAT it has 121% in
the price now. So the price before VAT is €500/121 x 100 = €413.22, and the price
with a 18% reduction is €500 /100 x (100 – 18) = €410.
18% off the sale price is cheaper than having the 21% VAT removed.
18) 20%
19)80% (Notice that 14 + 56 = 70 and 20 + 80 = 100 )
20) 4%
21) 25%
22) If I earn €7 tax is €1. 14% of €7 is 98c which is slightly cheaper.
23) This is a hard problem and is probably well beyond Junior Cert. It’s just here for
the fun! You can skip it if you like.
First we notice that every step of this involves adding a percentage; there is no step
when we add a fixed amount. ( For example the architect gets a percentage (10%) of
the building cost, the architect doesn’t get €50 plus a percentage. )
Since adding a percentage is the same as multiplying we can treat the whole problem
as a ratio or use algebra.
Solutions for ‘Find 1%’ page 2
Ratio Method (only works for multiplying problems)
Imagine the building cost €100, the building VAT is €13.50. The architect gets €10
and the VAT is €2.10. The total cost is 100 + 13.50 +10 + 2.10 = €125.60 this was
what would happen if the building cost €100 and the architect gets €10.
What’s the ratio of 125.6 : 2512?
It’s 1 : 20, so we multiply all the numbers in our imaginary problem by 20 to get the
numbers for the answer. Therefore the architect gets €200.
Algebra Method
(This can work with more complicated problems including payments of fixed
amounts.)
Let’s start with the builder and imagine that they get Z euro. The builder adds 13.5%
and the bill from the builder is Z + Z/100 x 13.5
after VAT at 13.5%
The architect gets Z/10 euro and adds VAT at 21%, (Z/10) + (Z/10)/100 x 21
So the two bills add up to
Z + Z/100 x 13.5
+ (Z/10) + (Z/10)/100 x 21 =
Z( 1+ 13.5/100 + 1/10 + (1/10) x 21/100) = 1.256 x Z
So 1.256 x Z = €2,512, and so Z = €2,512 / 1.256 = €2,000
Therefore the architect gets €200.