Ratio and proportion
problem
Favourite
Two ladders
Age
14 to 16
Challenge level
Two ladders are propped up against facing walls. The end of the
first ladder is 10 metres above the foot of the first wall. The end
of the second ladder is 5 metres above the foot of the second wall.
At what height do the ladders cross?
problem
Favourite
Rule of three
Age
11 to 14
Challenge level
If it takes four men one day to build a wall, how long does it take
60,000 men to build a similar wall?
problem
Favourite
Pumpkin pie problem
Age
7 to 11
Challenge level
Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies?
problem
Favourite
Trapezium four
Age
14 to 16
Challenge level
The diagonals of a trapezium divide it into four parts. Can you
create a trapezium where three of those parts are equal in area?
problem
Favourite
Triangle in a triangle
Age
14 to 16
Challenge level
Can you work out the fraction of the original triangle that is covered by the inner triangle?
problem
Favourite
Mixing lemonade
Age
11 to 14
Challenge level
Can you work out which drink has the stronger flavour?
problem
Favourite
Ratios and dilutions
Age
14 to 16
Challenge level
Scientists often require solutions which are diluted to a
particular concentration. In this problem, you can explore the
mathematics of simple dilutions
problem
Favourite
One and three
Age
14 to 16
Challenge level
Two motorboats travelling up and down a lake at constant speeds
leave opposite ends A and B at the same instant, passing each
other, for the first time 600 metres from A, and on their return,
400 metres from B. How long is the lake?
problem
Favourite
Blackcurrantiest
Age
5 to 7
Challenge level
Can you decide whose drink has the strongest blackcurrant flavour
from these pictures?