**Weights and measures are used for solving problems** in day to day life. One example is when using a recipe. If the recipe is for two persons and you are making it for six, you'll need to know how to increase the amount of ingredients without ruining the meal!

We have a total of 8 sets of quizzes about solving problems. The first four are general, the second four involve money. As usual, they get progressively more difficult. It's important to know how to work with numbers in everyday life, and these quizzes will test your maths skills. It would be a good idea to play them until you have a perfect 10 out of 10 score on each - this will improve your knowledge and your chances of passing the 11-plus.

See how you get on with this quiz and when you feel confident, move onto the next one.

1.

Bill can run three times faster than Keith. If it takes Bill 45 minutes to run a certain distance, how long will it take Keith to run the same distance?

135 min

15 min

30 min

90 min

If Bill can run 3 times faster than Keith, then Keith will take 3 times longer to run the same distance as Bill. If it takes Bill 45 minutes to run a certain distance, it will take Keith 3 × 45 = 135 min

2.

It takes Anna 1 hour to walk 4 miles. How long will it take her to walk 12 miles?

12 hr

⅓ hr

¼ hr

3 hr

It takes her 12 ÷ 4 = 3 hours. You have to divide by 4 because you want to find out how many 'lots' of 4 there are in 12: each 'lot' equals 1 hour: this is the same as adding 'lots' of 4 to itself until you get to 12. Alternatively, since 12 miles is 3 times more than 4 miles, then she must take 3 hours to cover 12 miles. It's up to you how you solve these problems BUT always show your workings

3.

John wants to build a fence around his garden. The length of the perimeter of his garden is 30 m. If fencing is sold in lengths of 3 m, how many pieces of fencing will John require?

100

10

90

30

John will require 30 ÷ 3 = 10 pieces of fencing. You have to divide by 3 because you want to find out how many 'lots' of 3 there are in 30: each 'lot' equals the weight of 1 piece of fencing: this is the same as adding 'lots' of 3 to itself until you get to 30

4.

The letters ABC can be arranged in different ways, e.g. BAC. In how many different ways can the letters ABC be arranged?

5

4

8

6

Here are the six arrangements:

ABC

ACB

BAC

BCA

CAB

CBA

With problems like this, work in a column because it's easier to see what you are doing. Look at the columns carefully, and you should get an idea of how to tackle simple arrangements like this

ABC

ACB

BAC

BCA

CAB

CBA

With problems like this, work in a column because it's easier to see what you are doing. Look at the columns carefully, and you should get an idea of how to tackle simple arrangements like this

5.

A bottle contains 1,500 ml of orange juice. If a glass can hold 100 ml of juice, how many glasses of orange juice does the bottle contain?

15

150

1.5

100

The bottle contains 1,500 ÷ 100 = 15 glasses of orange juice. You have to divide by 100 because you want to find out how many 'lots' of 100 there are in 1,500: each 'lot' equals 1 glass: this is the same as adding 'lots' of 100 to itself until you get to 1,500

6.

A bag of potatoes weighs 5kg. How much will 12 bags of potatoes weigh?

25 kg

2.5 kg

60 kg

6 kg

If 1 bag weighs 5 kg, then 12 bags will weigh 12 times more than that one bag ∴ 12 bags of potatoes weigh 12 × 5 = 60 kg

7.

A bag of sweets weighs 250 g. If each bag contains 20 sweets, what is the weight of each sweet?

0.125 g

1.25 g

125 g

12.5 g

Each sweet weighs 250 ÷ 20 = 12.5 g. You have to divide by 20 because you want to find out how many 'lots' of 20 there are in 250 : each 'lot' equals the weight of 1 sweet: this is the same as adding 'lots' of 20 to itself until you get to 250

8.

Peter is building an extension to his house, and he has to carry the bricks from the front garden to the back garden. He requires 1,500 bricks to build it. If his wheelbarrow can hold 75 bricks, how many wheelbarrow loads of bricks is this?

50

20

15

150

The number of wheelbarrow loads of bricks = 1,500 ÷ 75 = 20. You have to divide by 75 because you want to find out how many 'lots' of 75 there are in 1,500: each 'lot' equals 1 wheelbarrow loads of bricks: this is the same as adding 'lots' of 75 to itself until you get to 1,500

9.

A water tank can hold 10,000 m^{3} of water. If 100 m^{3} water is supplied to a camping site every day, how long will it take for the tank to empty?

100 days

10 days

1,000 days

1 day

It will take 10,000 ÷ 100 = 100 days for the tank to empty. You have to divide by 100 because you want to find out how many 'lots' of 100 there are in 10,000: each 'lot' equals 1 day: this is the same as adding 'lots' of 100 to itself until you get to 10,000

10.

A bag of apples weighs 4,800 g. If there are 12 apples in the bag, what is the weight of each apple?

4,000 g

0.4 g

40 g

400 g

The weight of each apple 4,800 ÷ 12 = 400 g. You have to divide by 12 because you want to find out how many 'lots' of 12 there are in 4.8 kg: each 'lot' equals the weight of 1 apple: this is the same as adding 'lots' of 12 to itself until you get to 4,800 g