On this page you will find Math Problems that are fit for Primary School kids [Grade 7 / 12 year olds] . Some of it might be a bit to dearing, but we like to put our kids in dearing situations..... and please, do remember, we must rather use these problems, or any other, to teach our children, and not just to keep them busy. We want to invite you to take part in this project by using the form below or by visiting our Project Page or E-Mail us. Also, if you would like to leave us some comments or suggestions about our projects, you are welcome to do so - also on the Project Page.    One other thing! If you contribute to this page, please send the answers too.

1. Two pumps are used to fill a tank with a capacity of 3 kl. If pump A is used on its own it will take 12 minutes to fill the tank and if pump B is used alone it will take 15 minutes to fill the tank. How long will it take to fill the tank if both the pumps are used at once?

2. One day a duck flew over a lake on which a number of ducks were swimming. The duck in the air said: "Good morning, you hundred ugly ducklings!" One of the ducks on the lake answered: "We are not a hundred! Us and the same number of us plus half of us plus a quarter of us together with you will be a hundred, you stupid duckling!" How many ducks were on the lake?

3. According to their father's will Eiknod must inherit a third of his father's donkeys, Onkied a quarter, Kiedon a fifth and Dienko a sixth. Their father died and he left them 57 donkeys and they could not see how to divide the heritage among themselves. Why not? Then came the clever neighbour and he made a plan: "You were always good to me; so now I will lend you three of my donkeys. Then you will have 60 to divide." Eiknod got 1 third of 60 = 20, Onkied got 1 quarter   60 = 15, Kiedon got 1 fifth of 60 = 12 and Dienko got 1 sixth of 60 = 10. Altogether they all then had 20 + 15 + 12 + 10 = 57 donkeys and their neighbour could take his three donkeys back. Can you explain how this could happen?

4. Criticise the following statements and illustrate your answers with calculations:
a. If the price of gold increases by 10% and then drops by 10%, the price is the same as before the rise.
b. Over the past year the price of bricks rose by 10%, the price of cement by 5% and wages by 15%. The total cost of building a home therefore rose by 30%.
c. The price of gold dropped by 100%.

5. A manufacturer of toys sells an article to a wholesaler at a profit of 20%, the wholesaler sells it to the retailer at a profit of 25%, and the retailer sells it to the consumer at a profit of 30%. Calculate what the consumer pays for the article if the production cost to the manufacturer is R51,69.

6. The interest rate at a certain bank changed from 21,5% to 22,75%. What was the percentage increase?

7. If there is an 11% increase on the sales tax rate of 12%, what will the new rate be?

8. Imagine that you have inherited R1 million from somebody. After you have shopped around properly, you have decided to invest your money at the safest bank you could find. This bank pays you an interest rate of 11% per year.
a. How much interest will you receive after one year?
b. How much will you have after one year?
c. Predict the strength of your investment for 5 years. We also expect that the interest rate will stay the same for this period and accept that you use none of your investment.
d. If we use the same conditions as with c., after how many years will your investment be just more than R2 million? If we use the same conditions as above, how much will your investment be after 15 years?

9. Give only the answers to the following calculations as a percentage:
a. 96,7% + 21,8%
b. 96,7% - 21,8%
c. 20% x 25%
d. 20% ÷ 25%
e. Increase 50% by 10%
f. What is the percentage decrease from 16% to 12%?

10. Number sequences:
a. Natural numbers: 1; 2; 3; 4; 5; ..... What is the thousandth natural number?
b. Even numbers: 2; 4; 6; 8; 10; .... What is the thousandth even number?
c. Odd numbers: 1; 3; 5; 7; 9; .... What is the thousandth odd number?
d. Square numbers: 1; 4; 9; 16; ... What is the thousandth square number?
e. Triangular numbers: 1; 3; 6; 10; 15; .... What is the thousandth triangular number?
f. Prime numbers: 2; 3; 5; 7; 11; 13; .... What is the thousandth prime number?
g. Fibonacci-numbers: 1; 1; 2; 3; 5; 8; 13; .... What is the 50h Fibonacci-number?
h. Cube numbers: 1; 8; 27; 64; 125; .... What is the thousandth cube number?
i. Rectangular numbers: 2; 6; 12; 20; 30; ... What is the thousandth rectangular number?
j. Powers of two: 1; 2; 4; 8; 16; .... What is the 50th power of two?
k. Powers of three: 1; 3; 9; 27; 81; .... What is the thousandth power of three?
l. Multiples of three: 3; 6; 9; 12; .... What is the thousandth multiple of three?
m. Factors of thousand: 1; 2; 4; 5; 8; 10; 20; 25 .... What is the thousandth factor of thousand?

11. What is the sum of the first ...
a. 100 Natural numbers: 1 + 2 + 3 + 4 + 5 + ..... =
b. 100 Even numbers: 2 + 4 + 6 + 8 + 10 + .... =
c. 100 Odd numbers: 1 + 3 + 5 + 7 + 9 + .... =
d. 100 Square numbers: 1 + 4 + 9 + 16 + ... =
e. 100 Triangular numbers: 1 + 3 + 6 + 10 + 15 + .... =
h. 100 Cube numbers: 1 + 8 + 27 + 64 + 125 + .... =
i. 100 Rectangular numbers: 2 + 6 + 12 + 20 + 30 + ... =
j. 40 Powers of two: 1 + 2 + 4 + 8 + 16 + .... =
k. 20 Powers of three: 1 + 3 + 9 + 27 + 81 + .... =
l. 100 Multiples of three: 3 + 6 + 9 + 12 + .... =

12. A man pays R196 for two pairs of pants and a shirt. If the shirt cost R81, what is the cost of one pair of pants?

13. Sinhg, a taxi owner asks R5 for each trip plus a certain amount per minute. What is the charge per minute if a trip of 6 minutes costs R23?

14. Nichol, another taxi owner asks R8 for each trip plus R2 per minute. After how many minutes will a trip with Sinhg and Nichol have the same cost?

15. A certain number added to four times the number gives 95. What is the number?

16. Five times a number is as much as twice the number plus 21. What is the number?

17. I double a number, add 5 and then multiply the answer by 4. My answer is then 1 less than eleven times the original number. Find the number with which I started.

18. John earns three times as much as Tom per week and Tom earns R60 less than John per week. What does each Tom earn per week?

19. If 3 is added to a number and the answer is multiplied by 5, the answer is the same as when the first number is multiplied by 7 and 3 is added to the answer. What is the original number?

20. A carpenter is making a built-in cupboard. It must be 1,71 m wide and have doors each 53 cm wide. The slats on either sides of each door should be of equal width. How wide should they be?

21. A box of apples weighs nine kilograms plus the weight of half a box of apples. What is the weight of a box of apples?

22. A man is now three times as old as his son and was 30 years old when his son was born. How old is the son now?

23. A man is four times as old as his son. Over six years he will be three times as old as his son. How old is the man now?

24. A man is now nine times as old as his son and will be five times as old as he in four years time. How old will the son be in four years time?

25. Two numbers differ by 2. Six times the smaller number is twice more than the larger number. Find the smaller number.

26. One number is three times the other, and four times the smaller plus two times the larger is 80. Find the smaller of the two.

27. The difference between two numbers is 56. The sum of these two numbers is 208. What is the smaller number of the two?

28. Jan has three times more marbles than Piet. If he gives 17 to Piet, he will have twice as many as Piet. How many marbles does Piet have?

29. There are 28 students in the class,two students sit at each desk.At the beginning of every month the teacher asks the students to change their seats so that every time the desk-mates are new and have never sit with each other. How many months can the students exchage their seats?

30. There are 555 weights with masses 1,2,3,...555 grams each. Distribute them into three equal heaps with equal mass.

31. If  Costas buys oranges at 5 for 2 cents and sell them at 4 for three cents, how many must he buy and sell to make a profit of  420 cents?

32.  At one of the stalls at a fair people were asked to guess how many peas there were in a bottle.  Someone quessed 163, another 169, someone else 178 and another someone 185.  One of these four was wrong with 1, another with 6, sobody else with 10 and another sombody with 16. How many peas were there in the bottle?

33.  Peter gave R50 to the post-office clerk and asked for some ten-cent stamps, twice as many twenty-cent stamps and five times as many thirty-cent stamps as ten-cent and twenty-cent stamps combined. How many of each did he get for R50?

34.  A boy was asked to think of a number, add 12, multiply by 4, subtract 4, find the square root, multiply by 5, subtract 2 and divide by 4. If his answer was 12, can you tell wth which number he started?

35. A boy was asked to think of a number, add 7, double the answer, subtract 6, divide by 2 and subtract the number he thought of eventually. The answer is 4. What was the number with which he started?

36. Koos and Jan ran against each other in the 100 m event. Koos won by 10 m. They then decided to race again, only this time Koos will give Jan a fairer chance and he started 10 m behind Jan. If they now run with the same speed as before, who will win the second race?

37. John runs the 800 m at a steady speed of 5 m/s. David runs the first 400 m at 1 m/s slower than John, and the second 400 m a 1 m/s faster than John. Who will win, and by how many seconds?

38. After a batsman has been out 5 times, his average is 60. He is out in his next innings, and his average then becomes 66. What did he score in this innings?

39. Three golfers named Tom, Dick and Harry are walking to the clubhouse. Tom always tells the truth, Dick sometimes tells the truth, while Harry never tells the truth. The guy in front says: "The guy in the middle is Harry." The guy in the middle says: "I'm Dick." The guy at the back says: "The guy in the middle is Tom." In what order are these three guys walking?

40. I mix 5 kg of a mixture containing 40% of cement and 60% of sand with a further 15 kg of sand. What will be the percentage of cement of the final mixture?

41. Three boys, Tom, Dick and Harry, after finishing a heavy meal, asked for a bowl of stewed prunes. While waiting for the prunes to be served, they fell asleep. After a while Tom woke up and found the prunes on the table. He ate what he thought was his share and went back to sleep. Then Dick woke up, ate what he thought was his share and fell asleep. Next Harry woke up and did what the other two had done. An hour later all three boys woke up and discovered eight prunes left in the bowl. How many prunes had been served originally?

42. The whole Malan family lived together on a farm. There were one grandma, one grandpa, two fathers, two mothers, four children, three grandchildren, one brother, two sisters, two sons, two daughters, one mother-in-law and one daughter-in-law. What is the smallest possible number of people that could be part of the family?

43. Koos, Kiewiet and Klaas divided a number of candy bars among themselves in the following way: Koos took halve of the bundel plus an extra halve. Kiewiet took halve of wat was left plus an extra halve. Klaas took halve of what was then left plus an extra halve. After this exactly one candy bar was left over which they divided among themselves so that each got another third. How many candy bars were there originally in the heap of candy bars?

44. Five sailors and their little monkey come across a heap of bananas and took it for themselves. They decided that they will divide it among them the following morning. That night, while all were asleep, one sailor got up and divide the heap in five and there was one banana left. He gave the remaining banana to the monkey, hided his own heap, put the other four heaps together and went to sleep again.

And so did it all happen, just the same, again with the second, third, forth and fifth sailors. Each one divide the heap in five, each time there was one remainder which was given to the monkey, each one hided his "share", put the other heaps together and nobody "knows" what everyone else did.

The next morning everyone knew that he cheated the other, but no one knew that everyone cheated everyone. They again divide the heap in five and again there was a remainder of one which was given to the monkey. How many bananas were there originally in the heap?

45.  If 1 fedal is equal to 11 kedals and 1 kedal to 27 redals, would you accept 6000 redals for 19 fedals? Why?

46.  A battalion of 1035 soldiers was made up of four companies. Each compony consists out of five platoons. Each platoon contained four squads. Each company had the same number of soldiers, as did each platoon and each squad. The commanders, second-in-commands, sergeant-majors or sergeants of the battalion, companies and platoons are respectively not members of a company, a platoon or a squad. How many soldiers were in each squad?

47.   The number of days of a normal year in an unique number because it is the sum of three consecutive square numbers and also the sum of the next two square numbers. What is this set of numbers?

48.  When she died Martha's age was 1/31 of her birth date. How old was she in 1900?

49.  Divide 45 into four parts so that when two are added to the first, subtracted from the second, multplied by the third and the fourth divided by two the result of each operation will be the same.

50.  You are asked to produce a length of rope which could be cut in four pieces so that: The first piece should be as long as the combined lengths of the second and third. The second is to be twice the length of the third. The third is to be as long as the length of the first less the length of the fourth. The fourth is to be two metres long plus one third of its own length. How long a piece of rope do you require?
source: http://www.wcape.school.za/niko/nicemath.htm