Maths week - Teacher’s problems (Revised)
There will be a problem for teachers each day in the notices. Teacher’s answers should be
submitted in writing to the HOD who will award a prize to the teacher who gets the most correct
by the end of the week. Note: answers will only be accepted on the day that the problem is
published
Monday
The cold water tap of a bathtub can fill the tub in 15 minutes. The drain, when opened, can
empty the full tub in 20 minutes.
If the tub is empty and the tap and drain are both opened at the same time, how long will it
take to fill the tub?
Tuesday
What are the two missing numbers?
Wednesday
If the pattern continues, what number is next?
a.
b.
c.
d.
e.
24
32
8
4
3495
80640
518567
40
48
12
6
4953
11520
1977
56 . . .
18
9...
9534 . . .
1920
384 . . .
76858157 817 . .
Thursday
If you start with the number 2 and place the digit 1 at the beginning of it you get 12, which is
exactly 6 times the number you start with.
a. Can you find a number that when you place the digit 1 at the beginning of it, you get a number
3 times the number you started with?
b. Can you find a number that when you place the digit 1 at the beginning of it, you get a number
5 times the number you started with?
c. Can you find a number that when you place the digit 1 at the beginning of it, you get a number
7 times the number you started with?
Friday
Davis decides to wear a different combination of clothes to work each day of one week. He is
required to wear trousers, shirt and tie.
What is the minimum number of shirts, ties and trousers he needs to do this?