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Find out what the brown box weighs in question 7.

Solving Problems (Medium)

This 11 Plus Maths quiz helps pupils practise solving problems using ratio, scaling, and logical reasoning to find patterns in real-life situations.

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Fascinating Fact:

A baker uses 3 cups of flour to make 12 muffins. To make 24 muffins, they need 6 cups of flour.

In 11 Plus Maths, pupils develop skills to solve word problems using reasoning and arithmetic. Scaling up or down helps in everyday tasks, like following recipes or doubling ingredients.

Key Terms

Ratio: A comparison showing how much of one thing there is compared to another.
Proportion: A relationship that shows two ratios are equal in value.
Scaling: Increasing or decreasing quantities while keeping the same proportions.

Learn more about 11 Plus preparation in our guide for parents.

Frequently Asked Questions (Click to see answers)

How does ratio help in solving maths problems?

Ratios help compare amounts and work out how to scale numbers up or down, like adjusting a recipe or measuring ingredients for more servings.

What are common problem types in the 11 Plus Maths test?

Questions often involve time, money, fractions, and scaling problems that require pupils to apply maths to real-life scenarios.

How can I improve my problem-solving skills?

Practise reading questions carefully, identify what’s being asked, and draw simple diagrams or lists to organise the information clearly.

Try These Related Quizzes

1 .

The circumference of a wheel is 24 cm. How many complete revolutions (turns) will it make in travelling 24 m?

100

1,000

First convert 24 m to centimetres: 24 × 100 = 2,400 cm. The number of revolutions (turns) = 2,400 ÷ 24 = 100. You have to divide by 24 because you want to find out how many 'lots' of 24 there are in 2,400: each 'lot' equals 1 turn: this is the same as adding 'lots' of 24 to itself until you get to 2,400

2 .

If the area of a square field is 144 m², what is the length and width of the field?

11 m

14 m

13 m

12 m

The length and width of the field are the same because the sides of a square are the same. You need to find a number which when multiplied with itself gives 144 because area = length × width: 12 × 12 = 144

3 .

If 12 people are served every two minutes in a fast food shop, how many people will have been served in 1 hour?

720

360

120

There are 60 minutes in an hour. 60 ÷ 2 = 30. You have to divide 60 by 2 because you want to find out how many 'lots' of 2 there are in 60: each 'lot' equals 12 people: this is the same as adding 'lots' of 2 to itself until you get to 60. Thirty 'lots' means that 30 × 12 = 360 people are served every hour

4 .

In a certain child's game, pushing a stick into a hole to a depth of 2 cm causes a wheel to turn through half a rotation (turn). How many complete rotations will the wheel turn through if the stick is pushed to a depth of 12 cm?

3 rotations

6 rotations

1.5 rotations

9 rotations

12 ÷ 2 = 6. You have to divide 12 by 2 because you want to find out how many 'lots' of 2 there are in 12: each 'lot' equals half a rotation: this is the same as adding 'lots' of 2 to itself until you get to 12. Six 'lots' means 6 × 0.5 = 3 complete rotations. DON'T forget, half a rotation = 180°

5 .

If a piece of material of length 4 m is folded in half on itself four times, what will the final length of the material be in centimetres?

6.25 cm

12.5 cm

25 cm

50 cm

First convert 4 m to centimetres: 4 × 100 = 400 cm. Folding in half four times, means that the length of the material decreases by a half four times:
400 ÷ 2 = 200
200 ÷ 2 = 100
100 ÷ 2 = 50
50 ÷ 2 = 25
This is the same as calculating 400 ÷ (2 × 2 × 2 × 2) = 400 ÷ 16 = 25 cm

6 .

If each box holds 12 items, how many boxes are required to hold 96,000 items?

8,000

800

800,000

The number of boxes required = 96,000 ÷ 12 = 8,000. You have to divide 96,000 by 12 because you want to find out how many 'lots' of 12 there are in 96,000 : each 'lot' equals 1 box: this is the same as adding 'lots' of 12 to itself until you get to 96,000

7 .

The brown box weighs eight times more than the black box. If the black box weighs 8 kg, what does the brown box weigh?

64 kg

8 kg

6.4 kg

0.8 kg

The brown box weighs eight times more than the black box which weigh 8 kg ? the brown box weighs 8 × 8 = 64 kg

8 .

A paperback book has 1,000 pages. If the book weighs 785 g, what is the weight of a single page? (You may ignore the front and back covers of the book.)

78.5 g

0.785 g

0.758 g

7.85 g

A single page weighs 785 ÷ 1,000 = 0.785 g. You have to divide 785 by 1,000 because you want to find out how many 'lots' of 1,000 there are in 785: each 'lot' equals 1 page

9 .

The French writer Jules Verne wrote the adventure novel 'Twenty Thousand Leagues Under the Sea'. If 1 league = 5.556 km, how many leagues is 2,778 km?

500

5,000

50,000

2,778 km = 2,778 ÷ 5.556 = 500 leagues. You have to divide 2,778 by 5.556 because you want to find out how many 'lots' of 5.556 there are in 2,778 : each 'lot' equals 1 league: this is the same adding 'lots' of 5.556 to itself until you get to 2,778 . By the way, it's a great read!

10 .

Some workers are filling up sacks with quality garden soil. If each sack can hold 25 kg, how many sacks can be filled from 1,250 kg of quality soil?

500

5,000

The number of sacks that can be filled = 1,250 ÷ 25 = 50 sacks. You have to divide 1,250 by 25 because you want to find out how many 'lots' of 25 there are in 1,250: each 'lot' equals 1 sack: this is the same as adding 'lots' of 25 to itself until you get to 1,250

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)