 If you lose a half of an eighth of all your money, what fraction of your money have you lost?

# Solving Problems (Difficult)

You should have learnt a few methods for solving real life problems from the previous three groups of 11-plus Maths quizzes: see how well you can apply your skills to these problems.

This is a difficult group of quizzes compared to the previous ones, so remember to read the questions carefully. Look at the four options before choosing your answer.

You may find it helpful to have pencil & paper by your side so you can jot any notes down. Take your time and if you get any wrong, read the helpful comment that appears after you've answered the question - this should help when playing the quiz again.

If you haven't already, it would be a good idea to do the previous quizzes BEFORE doing this one.

Good luck!

1.
The temperature of a substance in a chemistry experiment is -6°C. If the temperature is increasing at the rate of 2°C per minute, what will the temperature of the substance be in 8 minutes?
16°C
22°C
-4°C
10°C
If the temperature is increasing at the rate of 2°C per minute, the temperature of the substance at the end of 8 minutes = 8 × 2 = 16°C BUT it was initially at -6°C, so the final temperature will be -6°C + 16°C = 10°C
2.
If a wheel rotates (turns) at a speed of 6,000 revolutions (complete turns) in 5 minutes, how many revolutions does it make in 1 minute?
3,000
12,000
30,000
1,200
6,000 ÷ 5 = 1,200. You have to divide 6,000 by 5 because you want to find out how many 'lots' of 5 there are in 6,000 : each 'lot' equals the number of revolutions in 1 minute
3.
The height of the Towers building is three times taller than the Spire building. If the Spire building is 18 m high, how high is the Towers building?
6 m
54 m
36 m
27 m
The height of the Towers building is three times the height of the Spire building = 3 × 18 = 54
4.
Small toy cars are packed in toy boxes whose volume is 120 cm3. There are 6,000 toy boxes. If the toy boxes are to be packed into larger packing boxes, each of whose volume is 1,200 cm3, how many packing boxes will be required to pack all the toy boxes?
60
600
120
60,000
1,200 ÷ 120 = 10. You have to divide 1,200 by 120 because you want to find out how many 'lots' of 120 there are in 1,200: each 'lot' equals the number of toy boxes that can be put into each packing box. Each packing box can hold ten toy boxes, so 6,000 toy boxes require 6,000 ÷ 10 = 600 packing boxes: You have to divide 6,000 by 10 because you want to find out how many 'lots' of 10 there are in 6,000: each 'lot' equals the number of packing boxes that are required
5.
Mike lives five times further way from London than Tom. If Mike lives 75 miles away from London, how far away does Tom live?
375 miles
37.5 miles
15 miles
13 miles
If Mike lives five times further way from London than Tom, then Tom lives one fifth of that distance away from London: 75 ÷ 5 = 15 miles
6.
Farmer Jones is spraying his crops with a pesticide. If 10 ml of pesticide is required for each square metre, how many litres of pesticide will be required to spray 1,000 m2?
100 L
1 L
10 L
1,000 L
1 m2 requires 10 ml ∴ 1,000 m2 requires a 1,000 times more pesticide: 1,000 × 10 = 10,000 ml. Now 1 L = 1,000 ml ∴ 10,000 ml = 10 L because 10,000 ml is 10 times more than 1,000 ml
7.
At the end of a rugby match, 125 people left the grounds every 3 minutes. If there were 2,500 spectators at the match, how long did it take for the grounds to empty?
60 min
30 min
120 min
20 min
2,500 ÷ 125 = 20. You have to divide 2,500 by 125 because you want to find out how many 'lots' of 125 there are in 2,500 : each 'lot' equals 3 minutes. So 20 'lots' of 3 minutes means it took 20 × 3 = 60 minutes to empty the grounds. How fast or how slow something is happening is called a 'rate'. In this case: the spectators are leaving at a rate of 125 people per 3 minute period
8.
If you lose a half of an eighth of all your money, what fraction of your money have you lost?
14
116
18
34
The word 'of' means multiply, so 12 × 18 = 116
9.
It takes 4 men 128 hours to complete a certain engineering maintenance job. How long will it take 16 men to complete the same job if they work at the same speed?
64 hr
16 hr
32 hr
8 hr
It takes 4 men 128 hours to complete the job, so it will take 1 man four times that amount of time = 4 × 128 = 512 hr. Now a group of 16 men is 16 times more than one man, so they will complete the job in 116 of the time it takes one man: 512 ÷ 16 = 32 hr. ALTERNATIVELY, a group of 16 men is 4 times that of a group of 4 men, so they will do the job in quarter of the time: 128 ÷ 4 = 32 hr
10.
The temperature changed from -8°C to 3°C and then to -14°C over the last two day period. How many degrees below 3°C was the final temperature?
-14°C
14°C
-17°C
17°C
From 3°C to -14°C is a temperature movement of 17°C BUT it is not -17°C
Author:  Frank Evans