IMO Maths Olympiad Online Mock Test Class 10 Set C

1. A railway half ticket costs half the full fare. But, the reservation charges are the same on the half ticket as on the full ticket. One reserved first class full ticket from Mumbai to Ahmedabad costs Rs. 216 while one full and one half reserved ticket costs Rs. 327. What is the value of the first class full ticket and what is the reservation charge respectively?

2. In a Printing House, machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 a.m. While machine P is closed at 11 a.m. and the remaining two machines complete the work. Approximately at what time will the work be finished ?

3. Mohit went from Delhi to Shimla via Chandigarh by car. The distance from Delhi to Chandigarh is 3/4 times the distance from Chandigarh to Shimla. The average speed from Delhi to Chandigarh was one and a half times that from Chandigarh to Shimla. If the average speed for the entire journey was 49 km/hr, what was the average speed from Chandigarh to Shimla?

4. A trader marks his goods at 20% above the cost price. He sold half the stock at the marked price, one quarter at a discount of 20% on the marked price and the rest at a discount of 40% on the marked price. His total gain is ______.

5. A, B and C starts cycling around a circular path in the same direction at same time. The circumference of the path is 2400 m. If the speed of A is 300 m/min, speed of B is 480 m/min and C is 150 m/min and they start from the same point, then after what time interval they will be together at the starting point ?

6. A cake of 6 cm radius is divided into 3 sectors with central angles 120°, 150° and 90° respectively. The ratio of the areas of the three sectors is ____.

7. Two customers are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any one day as one another. Find the probability that both will visit the shop on (i) the same day, (ii) consecutive days.

8. There are three pipes fitted in a tank. First two pipes when operated simultaneously, fill the tank in the same time as filled by the third pipe alone. The second pipe fills the tank 7 hours faster than the first pipe and 3 hours slower than the third pipe. The approximate time required by each pipe to fill the tank simultaneously is _____.

9. A plot of land in the form of a rectangle has a dimension 240 m × 180 m. A drainlet 10 m wide is dug all around it (on the outside) and the earth dug out is evenly spread over the plot, increasing its surface level by 25 cm. The depth of the drainlet is _______.

10. Garima purchased a briefcase with an additional 10% discount on the reduced price after deducting 20% on the labelled price. If the labelled price was Rs. 1400, at what price did she purchase the briefcase?

11. What is more favourable for a buyer - discount series P of 20%, 15% and 10% or a discount series Q of 25%, 12% and 8% ?

12. Kruti took a loan at simple interest at 6 % in the first year with an increase of 0.5 % in each subsequent year. She paid Rs. 3375 as interest after 4 years. How much loan did she take?

13.

14. In the adjoining figure, M is the midpoint of BC and AE is half of BE, then AD is _____.

15. Three men, four women and six children can complete a work in seven days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete the work in 7 days ?

16. The sum of n terms of the three arithmetical progressions are S1, S2 and S3. The first term of each is unity and the common differences are 1, 2 and 3 respectively, then _____.

17. The given diagram represents some beams which supports part of a roof. If AC = 8metres, ∠BAC = 60°, ∠ACD = 30°, ∠ADC = 90° and ∠CAE = 90°, then the length of the beam AD is ______.

18. A number x is selected from the numbers 1, 2 & 3 and then a second number y is randomly selected from the numbers 1, 4 & 9. What is the probability that the product xy of the two numbers will be less than 9?

19. There are two examination rooms A and B. If 10 candidates are sent from A to B, the number of students in each room is the same. If 20 candidates are sent from B to A, the number of students in A is double the number of students in B. Find the number of students in each room.

20. A group of girls planned a picnic. The budget for food was Rs. 2400. Due to illness, 10 girls could not go to the picnic and cost of food for each girl increased by Rs. 8. How many girls had planned the picnic?

21. A circle of radius 'r' has been inscribed in a triangle of area A. If the semi-perimeter of the triangle be S, then ____.

22. A conical vessel of radius 6 cm and height 8 cm is filled with water. A sphere is lowered into the water and its size is such that when it touches the sides of the conical vessel, it is just immersed. How much water will remain in the cone after the overflow ?

23. The given pie chart shows the hourly distribution of all the major activities of a student. Find the difference between the time (in percent) the students spends in games and sleeping. Also, what is the difference in time (in hours) spent in school and in homework

24. The incomes of A, B and C are in the ratio 7 : 9 : 12 and their spendings are in the ratio 8 : 9 : 15. If A saves (1/4)th of his income, then the savings of A, B and C are in the ratio _____.

25. In the given figure, BD is the diameter of the circle with centre O, ∠COD = 92° and ∠ABD = 65°. Then y equals ______.

26. How many sides does a regular polygon have, whose interior angle is eight times its exterior angle?

27. The average of five consecutive natural numbers is m. If the next three natural numbers are also included, how much more than m will the average of these 8 numbers be ?

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29. A sports club has 130 members. An increase of 10% in the number of men and 20% in the number of women brought up the membership to 148. How many men and women were there originally?

30.

31. Select a figure from the options, which is not embedded in the given figure (X).

32. Machine 'A' produces 60% cloth and remaining is produced on machine 'B'. 25% of each machine's production is defective. Choose the diagram that best represents the situation. The shaded portion depicts defective cloth.

33. On a peculiar clock shown here, the hands move in an unusual way. Discover the system as revealed from the five positions, (i to v) shown below, and find the next position to be formed in fig (vi) from the options given below.

34. Select a figure from the options which satisfies the same conditions of placement of the dots as in figure (X)?

35. Find the missing term.

36. Which of the following options does not have the same relationship between them as is there between DH : EG ?

37. The question consists of a set of three figures X, Y and Z showing a sequence of folding of a piece of paper. Fig. (Z) shows the manner in which the folded paper has been cut. These three figures are followed by options from which you have to choose a figure which would most closely resemble the unfolded form of fig. (Z).

38. How many triangles are there in the figure below?

39. In a certain code language,
(i) 'pit na som' means 'bring me water'; (ii) 'na jo tod' means 'water is life';
(iii) 'tub od pit' means 'give me toy'; (iv) 'jo lin kot' means 'life and death';
Which of the following represents 'is' in that language ?

40. If in each of the following groups of numbers, last two digits are interchanged and after that they are arranged in descending order, then what will be the first digit of the middle group? 257, 491, 623, 846, 738

41. A college starts from 10 a.m. and continues till 1.30 p.m. In this duration there are 5 periods. If 5 minutes are provided before each period to leave the room and enter the other, then what is the duration of each period?

42. Find the missing number from amongst the given options at the place of sign of interrogation (?).

43. At an office where an interview was conducted to select persons for clerical posts, they came to know that out of 20 persons, 12 knew only typing and 5 knew only shorthand and the rest knew both typing and shorthand. Which of the following diagrams represents this fact?

44.

45. The given question is based on the symbols/numeric/alphabets as given below: If the first half of the above series is written in the reverse order, then which letter/symbol will be 7th letter from the left of 15th letter from right end.

46. Read the following information carefully and answer the question given below.
(i) There are five types of cards viz. A, B, C, D and E. There are three cards of each type. These are to be inserted in envelopes of three colours - Red, Yellow and Brown. There are five envelopes of each colour.
(ii) B, D and E type cards are inserted in red envelopes. A, B and C type cards are to be inserted in yellow envelopes and C, D and E type cards are to be inserted in brown envelopes.
(iii) T wo cards each of B and D type are inserted in red envelopes. Which of the following combinations of colour of the envelope and the number of cards is definitely correct in respect of E - type cards?

47. K is brother of N and X, Y is the mother of N, and Z is the father of K. Which of the following statements is not definitely true ?

48. If 'sand' is called 'air', 'air' is called 'plateau', 'plateau' is called 'well', 'well' is called 'island' and 'island' is called 'sky', then from where will a woman draw water?

49. Two ladies and two men are playing bridge a card game and seated at North, East, South and West of a table. No lady is facing East. Persons sitting opposite to each other are not of the same sex. One man is facing South. Which directions are the two ladies facing?

50. Some of the letters are missing which are given in that order as one of the options below it. Choose the correct option.
a __ n __ b __ __ ncb __ __ ncb