# 25 Math Olympiad For Primary Schools 2013

Here is the question of Mathematical olympiad for elementary students.

1. The ratio of the number of boys and girls in a school is 3 : 2. If 20% of the boys and 30% of the girls are scholarship holders, find percentage of the student who are not scholarship holders.

2. Two numbers are less than a third number by 30% and 37% respectively. How much percent is the second numbers less then the first?

3. A mixture of 40 litres of milk and water contain 10% water. How much water should be added to it so that water may be 20% in new mixture?

4. A customer asks for the production of x number of goods. The company produces y number of goods daily out of which z% are until for sale. The order will be completed in ….

5. The population of a town is 8.000. It increase by 10% during first year and by 20% during second year. The population after 2 years will be ….

6. In an examination, it is required to get 36% of maximum marks to pass. A student got 113 marks and was declared failed by 85 marks. The maximum marks are ….

7. A man spends 75% of his income. His income is increased by 20% and he increased his expenditure by 10%. His savings are increased by ….

8. In an examination, 52% of the candidates failed in English, 42% failed in Mathematis, and 17% in both. Find the number of those who passed in both the subjects.

9. If A’s income is 25% more than B’s and B’s income is 20% more than C’s, by what percent is A’s income more than C’s?

10. If the numerator of a fraction is increased by 20% and its denominator be diminished by 10%, the value of the fraction is . Find the original fraction.

11. For a sphere of radius 10 cm, the numerical value of the surface area in how many percent of the numerical value of its volume?

12. There are 300 girls who represent a certain school in both summer and winter sports. In summer 60% of these girls play cricket and the other 40% play squash. In writer the girls play hockey or netball but not both. 56% of the hockey players take cricket in summer and 30% of the cricket players take netball in winter. The number of girls who play netball and squash is

13. An energy conscious home owner makes three successive improvements that save, in turn, 20%, 25% and 55% on the heating cost of the house. The overall percentage saved is ….

14. In a school 30 boys and 20 giels entered a competition. Prize werw awarded to 10% of the boy and 20% of the girl. The total  percentage of entrants receiving prize was ….

15. Miss Evi had \$180. She spent 25% of the money on a shirt and 30% of the remainder on a dictionary. How much money had she left?

16. 50 books of equal thickness are stacked on top of one another. The stack of books is 230 cm high. If 14 books are removed from the stack, what is the remaining height of the books?

17.  Mrs Maria bought 36 cups at \$95 each and 12 bowls at \$1.50 each. She paid the cashier \$100. How much change did she receive?

18. A glass was   full water. From a similar glass that was   filled with water was poured into the first glass. What fraction of water was there in the first glass in the end?

19.    Find the two 10-digit numbers which becomes nine times as large if the order of the digits is reversed.
20.    Find the largest positif integer with the following properties:
(i)    all digits are different
(ii)    each two consecutive digits form a number divisible by either 17 or 23.
21.    If the number A19,993,11B is divisible by 72, find the difference between A and B.
22.    A number N is divisible by 90, 98 and 882 but it is not divisible by 50, 270, 686 and 1.764. It is known that N is a factor of 9,261,000. What is N?
23.    a is a number that has 8 different factor (including the number 1 and it self). What is the smallest possible value of a?

24. Among the integers 1, 2, …, 1,997, what is the maximum number of integers that can be selected such that the sum of any two selected number is not a multiple of 7?

25. The least number which when divided by 35, 45, 18 and 55 leaves a remainder 18, 28, 10 and 38 respectively is ….