Question 1
LEVEL 4
The time T (hours), required to build a brick wall is inversely proportional to the number of men M laying bricks.
When 6 men are laying bricks the wall takes 4 hours to build.
If it took \dfrac{3}{4} of an hour to build the wall how many men would there be?
Select the correct answer from the list below:
A: 12
B: 32
C: 40
D: 24
CORRECT ANSWER: B: 32
WORKED SOLUTION:
As it took 6 men a total of 4 hours to complete the wall that is a total of 6\times4=24 work hours.
To complete the wall in 0.75 hours that would require 24\div0.75=32 men working.
Question 2
LEVEL 4
5 friends are planing a camping trip.
They pack enough food to last all 5 friends 3 days.
2 of the friends decide not to go on the camping trip.
How long will the food last the remaining friends?
Select the correct answer from the list below:
A: 4 days
B: 6 days
C: 3 days
D: 5 days
CORRECT ANSWER: D: 5 days
WORKED SOLUTION:
As they took 3 days worth of food for a total of 5 people, that is a total of 5\times3=15 days worth of food for a single person.
If now only three friends are going camping that means there is 15\div3=5 days worth of food between them.
Question 3
LEVEL 4
5 friends want to go on a camping trip.
They are planning to bring 10 litres of water for all 5 friends for the trip.
A sixth person joins the trip.
How much water do they need for all 6 people?
Select the correct answer from the list below:
A: 8 litres
B: 16 litres
C: 10 litres
D: [12 litres
CORRECT ANSWER: D: 12 litres
WORKED SOLUTION:
As they took 10 litres of water for a total of 5 people, that is 10\div5=2 litres per person.
If now only another friend is going camping that means there needs to be 6\times2=12 litres of water in total.
Question 4
LEVEL 4
The time taken to check-in for a flight is inversely proportional to the number of airport staff working.
It takes 20 minutes for passengers to be checked-in when 8 staff are working.
How long will it take if 10 staff are working?
Select the correct answer from the list below:
A: 12 minutes
B: 14 minutes
C: 16 minutes
D: 18 minutes
CORRECT ANSWER: C: 16 minutes
WORKED SOLUTION:
As it took 8 staff a total of 20 minutes to complete the check in, that is a total of 8\times20=160 minuets of work.
If 10 staff are working, check in that would take 160\div10=16 minutes.
Question 5
LEVEL 4
At an archaeological dig site, the time it takes to cover an area of 1 square metre of area is inversely proportional to the number of scientists working on the site.
It takes 0.5 days to cover 1 square metre with 5 people working on it.
The total area of the dig is 24 metres squared.
Find how many people are needed to complete the dig in 3 days?
Select the correct answer from the list below:
A: 20
B: 15
C: 30
D: 25
CORRECT ANSWER: A: 20
WORKED SOLUTION:
As it took 5 people, half a day to cover 1 metre squared, that is a total of 5\times0.5=2.5 work days for an individual.
To complete total dig site of 24 metres squared days that would require a total 24\times2.5=60 work days.
Hence for this to be completed in 3 days, that would require 60\div3=20 people working.