So, you have made it to the third of our Difficult level Eleven Plus maths quizzes on Percentages – give yourselves a pat on the back! As you will know by now, percentages are a way to represent proportions of numbers, but how do you calculate them? In the last quiz we showed you one method. Here’s another which you might prefer:

What percentage of 70 is 28?

First divide 70 by 100 to work out what 1% of 70 is:

70 ÷ 100 = 0.7

Next, divide 28 by 0.7 to work out how many “lots” of 1% are in 28:

28 ÷ 0.7 = 40

So, there is your answer: 28 is 40% of 70

This method is great for estimating your answers, but it often requires a calculator!

So now, on with the quiz. You can use the method above, or the one we showed you in our previous quiz. Alternatively, you may have your own method. Use whichever you prefer – as long as it gives you the right answer!

1.

1,500 people were asked whether they prefer dogs or cats. 720 said “dogs”, 660 said “cats” and 120 said “neither”. What percentage of those surveyed prefer cats?

44%

33%

55%

66%

2.

A charity raffle sold 800 tickets for £1 each, making £800. They gave away £72 in prizes. What percentage of the money they raised went on prizes?

15%

13%

11%

9%

We are trying to find what percentage of 800 72 is:

(72 ÷ 800) × 100 = (72 × 100) ÷ 800 = 7,200 ÷ 800 = 9%

(72 ÷ 800) × 100 = (72 × 100) ÷ 800 = 7,200 ÷ 800 = 9%

3.

What percentage of 240 is 12?

2.5%

5%

10%

15%

(12 ÷ 240) x 100 = (12 × 100) ÷ 240 = 1,200 ÷ 240 = 5%

4.

What percentage of 8 is 30?

27%

375%

30%

350%

(30 ÷ 8) x 100% = (30 × 100) ÷ 8 = 3,000 ÷ 8 = 375%

In ‘top-heavy’ fractions (e.g.^{30}⁄_{8}), the percentage will be more than 100%

In ‘top-heavy’ fractions (e.g.

5.

What percentage of 72 is 48?

(Give your answer to two decimal places)

(Give your answer to two decimal places)

33.33%

60%

66.66%

70%

(48 ÷ 72) x 100 = (48 × 100) ÷ 72 = 4,800 ÷ 72 = 66.66%

If you know your times tables, you might have spotted that 72 is 6 x 12 and 48 is 4 x 12. 4 is two-thirds of 6 so the percentage will be equivalent to two-thirds, i.e. 66.66%

If you know your times tables, you might have spotted that 72 is 6 x 12 and 48 is 4 x 12. 4 is two-thirds of 6 so the percentage will be equivalent to two-thirds, i.e. 66.66%

6.

What percentage of 400 is 60?

1.5%

12.5%

15%

17.5%

(60 ÷ 400) × 100 = (60 × 100) ÷ 400 = 15%

Of course, you may have spotted that 400 is 4 x 100, so you could work this out more quickly by just dividing 60 by 4: 60 ÷ 4 = 15

Of course, you may have spotted that 400 is 4 x 100, so you could work this out more quickly by just dividing 60 by 4: 60 ÷ 4 = 15

7.

A survey asked 8,000 people in the UK which religion they followed. 1,840 said that they had no religion. What percentage does this represent?

19%

21%

23%

25%

(1,840 ÷ 8,000) x 100 = (1,840 × 100) ÷ 8,000 = 184,000 ÷ 8,000 = 23%

Don’t be put off by large numbers – they can often be rounded down by removing any zeros, e.g. 184,000 ÷ 8,000 is the same as 184 ÷ 8

Don’t be put off by large numbers – they can often be rounded down by removing any zeros, e.g. 184,000 ÷ 8,000 is the same as 184 ÷ 8

8.

What percentage of 900 is 81?

15%

13%

11%

9%

(81 ÷ 900) x 100 = (81 × 100) ÷ 900 = 8,100 ÷ 900 = 9%

Of course, 900 is 100 x 9, so you could work the answer out by simply dividing 81 by 9:

81 ÷ 9 = 9

Of course, 900 is 100 x 9, so you could work the answer out by simply dividing 81 by 9:

81 ÷ 9 = 9

9.

If 20% of us are vegetarian, how many vegetarians will there be in a randomly chosen group of 40 people (approximately)?

8

10

12

16

This question asks you to reverse the usual process:

To find 20% of 40, divide by 100 then times by 20:

40 ÷ 100 = 0.4

0.4 x 20 = 8

A quicker way to find 20% is to simply divide by 5 (because 20% is the same as one-fifth)

40 ÷ 5 = 8

To find 20% of 40, divide by 100 then times by 20:

40 ÷ 100 = 0.4

0.4 x 20 = 8

A quicker way to find 20% is to simply divide by 5 (because 20% is the same as one-fifth)

40 ÷ 5 = 8

10.

If there are 320 cars in a car park, and 96 of them are red, what percentage of cars in the car park are not red?

30%

55%

65%

70%

(96 ÷ 320) x 100 = (96 × 100) ÷ 320 = 9,600 ÷ 320 = 30%

That is the amount of red cars, but we want to know the percentage that are not red:

100 - 30 = 70, so 70% of the cars are not red

That is the amount of red cars, but we want to know the percentage that are not red:

100 - 30 = 70, so 70% of the cars are not red

(660 ÷ 1,500) x 100 = (660 x 100) ÷ 1,500 = 66,000 ÷ 1,500 = 44%