6. Practice Question Set B — Moderate/Exam Level (30 MCQs)

B1. The average of 11 numbers is 10.9. The average of the first six numbers is 10.5 and the average of the last six numbers is 11.4. Find the sixth number (common to both groups). (a) 10.5　(b) 11.0　(c) 11.5　(d) 12.0

B2. The average weight of 8 persons increases by 2.5 kg when a person weighing 65 kg is replaced by a new person. Find the weight of the new person. (a) 80 kg　(b) 82.5 kg　(c) 85 kg　(d) 87.5 kg

B3. The average age of a class of 40 students is 15 years. When the class teacher’s age is included, the average age of the class (now 41 members) increases by exactly 1 year. Find the teacher’s age. (a) 50 years　(b) 52 years　(c) 54 years　(d) 56 years

B4. A car covers a certain distance at 50 km/h and returns the same distance at 75 km/h. Find its average speed for the whole journey. (a) 55 km/h　(b) 58 km/h　(c) 60 km/h　(d) 62.5 km/h

B5. The average of 5 consecutive odd numbers is 61. Find the largest of these numbers. (a) 63　(b) 65　(c) 67　(d) 69

B6. In a school, the average weight of 30 boys is 45 kg and that of 20 girls is 40 kg. Find the average weight of all 50 students. (a) 41 kg　(b) 42 kg　(c) 43 kg　(d) 44 kg

B7. The average of three numbers is 42. The first number is twice the second, and the second number is twice the third. Find the first number. (a) 60　(b) 66　(c) 72　(d) 78

B8. Five years ago, the average age of a father and his son was 20 years. Find their present average age. (a) 22 years　(b) 23 years　(c) 24 years　(d) 25 years

B9. In an examination, the average marks of 60 candidates was 40. The average marks of those who passed was 50, and of those who failed was 30. Find the number of candidates who passed. (a) 25　(b) 28　(c) 30　(d) 32

B10. The average of 100 numbers was calculated as 45. Later, it was found that two numbers, 23 and 74, were wrongly copied as 32 and 47 respectively. Find the correct average. (a) 44.82　(b) 45.00　(c) 45.18　(d) 45.36

B11. A car covers four equal distances at speeds of 10 km/h, 20 km/h, 30 km/h and 60 km/h respectively. Find its average speed for the entire journey. (a) 18 km/h　(b) 20 km/h　(c) 22 km/h　(d) 24 km/h

B12. Find the average of the first 20 multiples of 7. (a) 70.5　(b) 71.5　(c) 72.5　(d) 73.5

B13. The average of 9 consecutive natural numbers is 20. Find the largest number among them. (a) 22　(b) 23　(c) 24　(d) 25

B14. The average height of 35 students in a class is 150 cm. When the class teacher’s height is included, the average height of the class increases by exactly 1 cm. Find the teacher’s height. (a) 178 cm　(b) 182 cm　(c) 184 cm　(d) 186 cm

B15. A batsman’s average after 16 innings is 36 runs. If he scores 70 runs in his 17th innings, find his new average. (a) 36 runs　(b) 37 runs　(c) 38 runs　(d) 39 runs

B16. The average weight of 15 students in a class increases by 2 kg when two students weighing 40 kg and 50 kg are replaced by two new students. Find the average weight of the two new students. (a) 55 kg　(b) 58 kg　(c) 60 kg　(d) 62 kg

B17. The average age of a group of 18 people is 32 years. A person aged 45 years leaves the group, and simultaneously a new person joins, keeping the group size at 18. If the new average age is 31 years, find the age of the new person. (a) 24 years　(b) 25 years　(c) 27 years　(d) 29 years

B18. A man travels to his office at a certain speed and returns by the same route at 1.5 times that speed. If his average speed for the entire journey is 42 km/h, find his speed while going to office. (a) 30 km/h　(b) 32 km/h　(c) 35 km/h　(d) 38 km/h

B19. A train covers 100 km at 50 km/h, 180 km at 60 km/h, and 150 km at 75 km/h. Find its average speed for the entire journey (nearest to one decimal place). (a) 60 km/h　(b) 61.4 km/h　(c) 62.5 km/h　(d) 63.8 km/h

B20. The average marks of three groups of students, consisting of 20, 30, and 50 students, are 60, 70, and 80 respectively. Find the average marks of all 100 students. (a) 71　(b) 72　(c) 73　(d) 74

B21. Find the average of the squares of the first 16 natural numbers. (a) 91.5　(b) 92.5　(c) 93.5　(d) 94.5

B22. Find the average of the cubes of the first 12 natural numbers. (a) 487　(b) 497　(c) 507　(d) 517

B23. In a college, the ratio of the number of boys to girls is 3:2. The average weight of boys is 65 kg and that of girls is 55 kg. Find the average weight of all the students. (a) 59 kg　(b) 60 kg　(c) 61 kg　(d) 62 kg

B24. Using the deviation (assumed mean) method, find the average of 1997, 2005, 1990, 2012, 1998, and 2008. (a) 2000.67　(b) 2001.00　(c) 2001.67　(d) 2002.33

B25. The average of 50 numbers was calculated as 38. It was later found that a number, 45, was misread as 54 while calculating the average. Find the correct average. (a) 37.62　(b) 37.82　(c) 38.18　(d) 38.42

B26. The average age of a company’s 30 employees is 34 years. Two employees, aged 50 and 55 years, retire, and simultaneously three new employees with an average age of 26 years join. Find the new average age of the company (31 employees). (a) 31.50 years　(b) 32.03 years　(c) 32.50 years　(d) 33.00 years

B27. The average of 11 consecutive multiples of 4 is 84. Find the smallest of these multiples. (a) 60　(b) 62　(c) 64　(d) 66

B28. A batsman has a certain average after 20 innings. In his 21st innings, he scores 30 runs, and this brings his average down by 2 runs. Find his average after the 21st innings. (a) 68 runs　(b) 69 runs　(c) 70 runs　(d) 71 runs

B29. The average of 8 numbers is 45. The average of the first 5 numbers is 42, and the average of the last 4 numbers is 50. Find the value of the 5th number (common to both groups). (a) 45　(b) 48　(c) 50　(d) 52

B30. The average age of a family of 5 members is 26 years today. One of these members, presently aged 33 years, married into the family exactly 3 years ago. Find the average age of the remaining 4 original family members three years ago. (a) 20.25 years　(b) 20.75 years　(c) 21.25 years　(d) 21.75 years