Mixture and Alligation, Mensuration, Data Interpretation, Probability, Permutation and Combination - Question Bank
1. The average temperature for the first three days of a week was 35°C. For the next four days, it was 38°C. What is the average temperature for the week?
2. A mixture contains alcohol and water in the ratio 4:3. If 5 liters of water are added to the mixture, the ratio becomes 4:5. What is the quantity of alcohol in the given mixture?
3. The area of a square is 64 sq cm. What is the length of its diagonal?
4. In how many ways can the letters of the word 'RACE' be arranged?
5. A bag contains 4 red and 6 blue marbles. If one marble is drawn at random, what is the probability of drawing a blue marble?
6. The average of 6 numbers is 20. If one number is added, the average becomes 22. What is the added number?
7. A rectangular sheet of paper has length 20 cm and breadth 15 cm. What is its perimeter?
8. In how many ways can 5 people be seated in a row?
9. What is the probability of getting a head when a coin is tossed?
10. A rectangular garden is 12 m long and 5 m wide. A path of uniform width of 2 m is made around the garden. What is the area of the path?
11. The sides of a triangle are in the ratio 3:4:5. If the perimeter is 60 cm, what is the length of the longest side?
12. How many ways can 5 different books be arranged on a shelf?
13. A bag contains 3 red balls and 4 blue balls. If two balls are drawn at random, what is the probability that one is red and one is blue?
14. The average of 5 numbers is 6. If one number is removed, the average becomes 5. What is the removed number?
15. Two trains are running in opposite directions, the first train passes a pole in 2 seconds and the second train passes the pole in 3 seconds. In how much time will they cross each other?
16. A train 150 m long is moving at 45 km/hr. In what time will it pass a platform 100 m long?
17. Two trains of equal length pass a pole in 10 seconds and 15 seconds respectively. In what time will they cross each other if they are moving in the same direction?
18. A car travels 100 km in 2 hours. What is its speed in meters per second?
19. A train travels at 60 km/hr. How many seconds will it take to travel 120 meters?
20. The radius of a circle is 21 cm. What is its area?
21. The perimeter of a square field is 400 m. What is the area of the field?
22. A rectangular field is 50 m long and 40 m wide. A path 2.5 m wide is constructed outside the field. What is the area of the path?
23. The length of a rectangular park is 100 m and its breadth is 75 m. What is the total cost of gravelling the path at Rs. 12 per sq m?
24. The area of a circular field is 1386 sq m. What is its radius?
25. The average age of a class of 30 students is 15 years. If the teacher's age is included, the average age increases by 1 year. What is the teacher's age?
26. The average marks of a student in 5 subjects are 72. If the marks in the sixth subject are added, the new average becomes 70. What are the marks in the sixth subject?
27. The average of 10 numbers is 30. If each number is multiplied by 5, what will be the new average?
28. The average of 5 numbers is 27. If one number is excluded, the average becomes 25. What is the excluded number?
29. The average weight of 8 men is increased by 1.5 kg when one of the men, whose weight is 65 kg, is replaced by a new man. What is the weight of the new man?
30. A shopkeeper sells 10 kg of sugar at Rs. 12 per kg and 15 kg of sugar at Rs. 10 per kg. What is the average price per kg of the mixture?
31. In how many ways can the letters of the word 'SUCCESS' be arranged?
32. How many permutations are there of the digits 1, 2, 3, 4, 5 taken all at a time?
33. In how many ways can a committee of 3 men and 2 women be formed from 7 men and 5 women?
34. How many different signals can be made by hoisting 3 red, 4 yellow and 2 blue flags on a pole?
35. In how many ways can the letters of the word 'APPLE' be arranged?
36. A number is chosen at random from the numbers 1 to 10. What is the probability that the number is prime?
37. In a class of 30 students, the probability of selecting a girl is 2/5. How many boys are there in the class?
38. What is the probability of getting a sum of 7 when two dice are rolled?
39. A bag contains 5 red balls and 7 blue balls. If two balls are drawn at random, what is the probability that both are red?
40. If a number is selected at random from the first 20 natural numbers, what is the probability that it is a multiple of 3?
41. The sum of two numbers is 12 and their product is 35. What are the numbers?
42. A right-angled triangle has a base of 6 cm and a height of 8 cm. What is its area?
43. The length of a rectangle is twice its breadth. If its area is 288 sq m, what is its perimeter?
44. A square has a side length of 10 cm. What is its area?
45. The perimeter of a rectangle is 40 cm. If the length is 12 cm, what is its breadth?
46. The area of a circle is 154 sq cm. What is its circumference?
47. In what ratio must rice at Rs. 7.20 per kg be mixed with rice at Rs. 5.70 per kg so that by selling the mixture at Rs. 8.50 per kg, there is a gain of 15%?
48. A shopkeeper mixes two types of tea, one costing Rs. 40 per kg and another Rs. 55 per kg. He sells the mixture at Rs. 54 per kg. What is the ratio in which he mixed the two types of tea?
49. Two alloys, A and B, contain copper and zinc in the ratio 3:5 and 1:4 respectively. In what ratio should the two alloys be mixed so that the resulting alloy has copper and zinc in the ratio 2:7?
50. A vessel contains a mixture of milk and water in the ratio 5:3. If 8 liters of milk are added to the mixture, the ratio becomes 11:6. What was the initial quantity of milk in the vessel?