PERCENTAGES

TIP: When doing these sort of problems, remember:

a) A percentage is just a fancy name for a proportion of 100.
    For example 16% of 100 = 16 (i.e. 16 in every 100). Whereas,
    16% of 200 = 32 (i.e. if there's 16 in every 100 then there's 32 in every 200),
    likewise 16% of 50 = 8. As a general formula:

    a% of b = b x a/100

b) You can work out percentage increases by learning formulas, but the easiest
    way is to use a bit of common sense and a bit of algebra (which you need to
    know anyway).

    If after a 10% increase something (call this x) = 200.
    then we can write this as:

    x + (10% of x) = 200

    we know what 10% of x is from the formula in a), so:

    x + 0.1x = 200

    Now do a bit of algebra, to find x:

    x(1 + 0.1) = 200
    x = 200/1.1 =  181.82
      

c) Percentage decreases can be workd out in the same way:

   If after a 10% decrease something = 270

   we get x(1 - 0.1) = 270

   x = 270/0.9 = 300
     

Solve the following:

1.  Tim bought a new car in 1995 for £10,000 in 2000 the car was priced at
     £12,500. Calculate the percentage increase in the price of the car over
     the five years.

2.  "Jeans 'R' Us" have a sale of Jeans and T-shirts, they have 120 items in the
      sale. The Jeans and T-shirts are in the ratio 5 : 3

     What percentage of the items in the sale are Jeans?

3.  A shop has a 3 day sale where each day, prices are reduced by 10% of the
     price on the previous day. Before the start of the sale a freezer is priced at
     £300. On the first day of the sale the price of the freezer is reduced by
     10%.

     a) How much is the freezer priced at on the first day of the sale?
     b) How much is the freezer priced at on the last day of the sale?

     On the first day of the sale a video recorder is priced at £200.

     c) How much was the video recorder before the sale?

 

4.  Bill shares £180 between his two neices Katie and Amelia. The Ratio of      Katie's share to Amelia's share is 5:4.

    a) How much is Katie given?
    b) How much is Amelia given?

    Katie then gives 10% of her share to Amelia.

    c) What percentage of the £180 does Amelia now have?

 

5. The most expensive bike at the mountain bike shop can be bought for £560
    or it can be payed for with a 25% deposit and 10 monthly payments of £42.
 
    How much extra do you need to pay in interest if you opt to pay over 10
    months?
 
    

6. An advertisement for the new multi-media PC says that the computer is only
    £799.00 (excluding VAT). If VAT is added at the rate of 17.5% of the
    selling price, how much do you actually have to pay for the computer when
    VAT is added?

7. After two years the value of a tractor has fallen to £15,000. After each year
    passes the depreciation (loss in value) of the tractor has been calculated at
    10%.

    a) What was the value of the tractor after the first year?
    b) What was the original cost of the tractor?

 

8. Business is looking good at "e-Systems" so they have decided to increase
    their workforce by 20% to cover all the new orders coming in. Before
    recruiting any new employees, 60 people were working at "e-Systems".

    a) Assuming the company could recruit all the people they wanted,
        how many were then working at "e-Systems"?


    b) If the company found that they could only recruit 75% of the people they
        wanted, how many were then working at "e-Systems"?

 

Ok Here's the Answers