Topic – Average - Rates Class – 8 1. Find the average of first 7 whole numbers. 2. Find the average of first 5 natural numbers. 3. Find the average of first 4 prime numbers. 4. Find the average of the following numbers : 7, 19, 31, 43, 70 5. Find the arithmetic mean of the numbers 3, 0, -1, 7 , 11 6. Find the mean of first 10 odd natural numbers 7. Find the mean of first 10 even natural numbers 8. The mean of first 5 multiples of 2 is _______ 9. Mahesh obtained the following marks on a set of math’s tests: 80, 85, 90, 71, 60, and 100, what is his average score? 10. A cricketer scores the following runs in eight innings: 58, 76, 40, 35, 46, 45, 0, and 100. Find the mean score? 11. Find the mean of the following observations that were recorded during an experiment : 4, 6, 7, 5, 3, 5, 4, 5, 2, 6, 2, 5, 1, 9, 6, 5, 8, 4, 6, 7 12. The marks (out of 100) obtained by a group of students in a test are 85, 76, 90, 85, 39, 48, 56, 95, 81 and 75. Find the mean marks obtained by the group. 13. In the first 10 over’s of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 over’s to reach the target of 282 runs?
Transcript
Topic – Average - Rates
Class – 8
1. Find the average of first 7 whole numbers.
2. Find the average of first 5 natural numbers.
3. Find the average of first 4 prime numbers.
4. Find the average of the following numbers : 7, 19, 31, 43, 70
5. Find the arithmetic mean of the numbers 3, 0, -1, 7 , 11
6. Find the mean of first 10 odd natural numbers
7. Find the mean of first 10 even natural numbers
8. The mean of first 5 multiples of 2 is _______
9. Mahesh obtained the following marks on a set of math’s tests: 80, 85, 90, 71, 60, and 100, what is his average score?
10.A cricketer scores the following runs in eight innings: 58, 76, 40, 35, 46, 45, 0, and 100. Find the mean score?
11.Find the mean of the following observations that were recorded during an experiment : 4, 6, 7, 5, 3, 5, 4, 5, 2, 6, 2, 5, 1, 9, 6, 5, 8, 4, 6, 7
12.The marks (out of 100) obtained by a group of students in a test are 85, 76, 90, 85, 39, 48, 56, 95, 81 and 75. Find the mean marks obtained by the group.
13. In the first 10 over’s of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 over’s to reach the target of 282 runs?
14.A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
15.A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
16.The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
17.The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
18.The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
19.The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is?
20.The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is?
21.A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per liter for three successive years. What approximately is the average cost per liter of petrol if he spends Rs. 4000 each year?
22. In Arun's opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?
23.The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is?
24.The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.
25.A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:
26. If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is:
27.A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is:
28.The average mark by 40 students of a class is 85. Difference in marks between the student with highest and the one with lowest marks is 108. If both these students are removed average falls by 1 mark .Find the highest mark?
29.Average score of 55 students is 88. If the top 4 students' score is excluded, average of remaining students drops by 4. if the second highest scorer scored
less than 133 and all students have integral scores , find the minimum marks that could have been scored by the topper
30.The average (arithmetic mean) of 3 numbers is 60. If two of the numbers are 50 and 60, what is the third number?
31. In a certain game, each of the 5 players received a score between 0 and 100 inclusive. If their average (arithmetic mean) score was 80, what is the greatest possible number of the 5 players who could have received a score of 50?
32.The average of nine numbers is 9. When a tenth number is added the average of the ten numbers is also 9. What is the tenth number?
33.The average (arithmetic mean) of the test scores of a class of p students is 70, and the average of the test scores of a class of n students is 92. When the scores of both classes are combined, the average is 86. What is the value of (p / n)?
34. If the average (arithmetic mean) of three different positive integers is 70, what is the greatest possible value of one of the integers?
35. It is 185 km between Chennai and Bangalore. If a bus takes 2 hours to travel the first 85 km, how long the bus has to take travel the final 100 km in order to average 50 km an hour for the entire trip?
36.The average (arithmetic mean) of a list of 6 numbers is 20. If we remove one of the numbers, the average of the remaining numbers is 15. What is the number that was removed?
37.Shelby went from her house to the mall at 7 km/hr and came back the same way at 12 km/hr. If the entire round trip took an hour, how far was the distance between the house and the mall?
38.John drove for 3 hours at a rate of 50 miles per hour and for 2 hours at 60 miles per hour. What was his average speed for the whole journey?
39.The average monthly salary of 12 workers and 3 managers in a factory was Rs. 600. When one of the manager whose salary was Rs. 720, was replaced with a new manager, then the average salary of the team went down to 580. What is the salary of the new manager?
40.The average wages of a worker during a fortnight comprising 15 consecutive working days was Rs.90 per day. During the first 7 days, his average wage was Rs.87 per day and the average wage during the last 7 days was Rs.92 per day. What was his wage on the 8th day?
41.The average of 5 quantities is 6. The average of 3 of them is 8. What is the average of the remaining two numbers?
42.The average temperature on Wednesday, Thursday and Friday was 250. The average temperature on Thursday, Friday and Saturday was 240. If the temperature on Saturday was 270, what was the temperature on Wednesday?
43.The average age of a group of 12 students is 20 years. If 4 more students join the group, the average age increases by 1 year. The average age of the new students is.
44.When a student weighing 45 kg left a class, the average weight of the remaining 59 students increased by 200g. What is the average weight of the remaining 59 students?
45.Three math classes: X, Y, and Z, take an algebra test. The average score in class X is 83. The average score in class Y is 76. The average score in class Z is 85. The average score of all students in classes X and Y together is 79. The average score of all students in classes Y and Z together is 81. What is the average for all the three classes?
46.The average weight of a class of 24 students is 36 years. When the weight of the teacher is also included, the average weight increases by 1kg. What is the weight of the teacher?
47.The average of 5 quantities is 10 and the average of 3 of them is 9. What is the average of the remaining 2?
48.The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member?
49.A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the boy interchanges the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one. What was the difference of the two digits a and b?
50.Average cost of 5 apples and 4 mangoes is Rs. 36. The average cost of 7 apples and 8 mangoes is Rs. 48. Find the total cost of 24 apples and 24 mangoes.
51.Average weight of 25 boys in a class is 48 kg. The average weight of the class of 40 students is 45 kg. What is the average weight of the 15 girls in the class?
52.There are two sections A and B of a class, consisting of 36 and 44 students respectively. If the average weight of sections A is 40 kg and that of section b is 35 kg. Find the average weight of the whole class?
53.A batsman makes a score of 87 runs in the 17th inning and thus increases his averages by 3.Find his average after 17th inning?
54.A student was asked to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of x?
55.David obtained 76, 65, 82, 67 and 85 marks (out in 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
56.The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
57.Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of the train during the whole journey?
58.The average age of 36 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years?
59.The average of five numbers id 27. If one number is excluded the average becomes 25. The excluded number is
60.The batting average for 40 innings of a cricket player is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, the average of the remaining 38 innings is 48 runs. The highest score of the player is
61.The average score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches are 42. Then find the average for the last four matches?
62.A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is
63.A motorist travel to a place 150 km away at an average speed of 50 km/hr and returns at 30 km/hr. His average speed for the whole journey in km/hr is
64.The average age of a husband and his wife was 23 years at the time of their marriage. After five years they have a one year old child. The average age of the family now is
65. In an examination, a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his history paper, his average per paper would have been 65. How many papers were there in the examination?
66.The average salary of all the workers in a workshop is Rs.8000. The average salary of 7 technicians is Rs.12000 and the average salary of the rest is Rs.6000. The total number of workers in the workshop is
67.After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member?
68.The marks of seven students in a mathematics test with a maximum possible mark of 20 are given below: 15, 13, 18, 16, 14, 17, and 12. Find the mean of this data set.
69.The average age of a class of 30 students is 12. If the teacher is also included the average becomes 13 years. Find the teacher’s age.
70.The average of 13 papers is 40. The average of the first 7 papers is 42 and of the last seven papers are 35. Find the marks obtained in the 7th paper?
71.The average age of the Indian cricket team playing the Nagpur test is 30. The average age of 5 of the players is 27 and that of another set of 5 players, totally different from the first five, is 29. If it is the captain who was not included in either of these two groups, then find the age of the captain.
72.A bus goes to Chennai to Bangalore at the rate of 60 km per hour. Another bus leaves Bangalore for Chennai at the same times as the first bus at the rate of 70 km per hour. Find the average speed for the journeys of the two buses combined if it is known that the distance from Chennai to Bangalore is 420 kilometers.
73.A train travels 8 km in the first quarter of an hour, 6 km in the second quarter and 40 km in the third quarter. Find the average speed of the train per hour over the entire journey.
74.The average weight of 6 men is 68.5 kg. If I is known that Ram and Tram weigh 60 kg each, find the average weight of the others.
75.The average score of a class of 40 students is 52. What will be the average score of the rest of the students if the average score of 10 of the students is 61.
76.The average age of 80 students of IIM, Calcutta of the 2005 batch is 22 years. What will be the new average if we include the 20 faculty members whose average age is 37 years?
77.Out of the three numbers, the first is twice the second and three times the third. The average of the three numbers is 88. The smallest number is
78.The average height of 30 girls out of a class of 40 is 160 cm and that of the remaining girls is 156 cm. The average height of the whole class is
79.The average weight of a group of 30 friends increases by 1 kg when the weight of their football coach was added. If average weight of the group after including the weight of the football coach is 31kgs, what is the weight of their football coach in kg?
80.Find the average of all the following numbers: 142, 147, 153, 165, 157
81.Find the average of all the following numbers: 4, 10, 16, 22, 28
82.Find the average of all the following numbers: 4, 10, 16, 22, 28, 34
83.The average mark of a student in 4 examinations is 40. If he got 80 marks in the 5th exam, then what is his new average?
84. In a group the average income of 6 men is 500 and that of 5 women is 280, then what is average income of the group?
85.The average weight of a class of 30 students is 40 kg, if the teacher’s weight is included then the average weight increases by 2 kg. Find the weight of the teacher?
86.The average age of Mr. and Mrs. Mohan 4 years ago was 28 years. If the present average age of Mr. and Mrs. Mohan and their son is 22 years. What is the age of their son?
87.The average price of 10 books is increased by Rs.17 when one of the book whose value is Rs.400 is replaced by a new book. Find the price of the new book?
88.The average mark of girls in a class is 62.5. The average mark of 4 girls among them is 60. The average mark of remaining girls is 63. Find the number of girls in the class?
89.Find the average of first 50 natural numbers?
90.Find the average if the first nine prime number is?
91.The average of 2, 7, 6 and m is 5 and the average of 18, 1, 6, m and n is 10. What is the value of n?
92.The average of a non-zero number and its square is 5 times the number, the number is?
93.A group of nine persons went to a hotel for taking their lunch. Eight of them spent Rs.12 each on their lunch and the ninth person spent Rs.8 more than the average expenditure of all the nine. What was the total amount spent by them?
94.The average weight of X, Y, Z is 45 kg. If the average weight of X and Y is 40 kg and that of Y and Z is 43 kg. Find the weight of Y?
95.The sum of three consecutive odd numbers is 48 more than the average of these numbers. What is the first of these three numbers?
96.A family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 67 years, that of parent is 35 years and that of the grand children is 6 years. What is the average age of the family?
97.A library has an average of 520 visitors on Sundays and 240 on other days. The average number of visitors per day in a month 30 days beginning with a Sunday is?
98.The average age of a class of 39 students is 15 years. If the age of the teacher is included, the average increases by 3 months. Find the age of the teacher?
99.The average weight of 10 crew members of a ship increases by 1.8 kg. When on of the crew member who weighs 53 kg is replaced with a new crew member. Find the weight of the new crew member.
100. A batsman makes a score of 87 runs in the 17th innings and increases his average by 3. Find his average after the 17th innings.
101. The average age of a class is 15.8 years. The average age of boys in the class is 16.4 years while that of the girls is 15.4. What is the ratio of boys to girls in the class?
102. In a cricket team (containing 11 members), the average age of eleven players is 28 years, the average ages of three groups of players each are 25 years, 28 years and 30 years respectively. If in these groups, the captain and the youngest player are not included and the captain is eleven years older than the youngest players, what is the age of the captain?
103. The average age of the boys in the class is twice the number of girls in the class. If the ratio of boys and girls in the class of 36 be 5 : 1, what is the total age of the boys in the class?
104. 5 years ago, the average age of X and Y was 15 years, average age of X, Y and Z today is 20 years, how old will Z be after 10 years?
105. The average weight of 3 men P, Q and R is 84 kg. Another man S joins the group and the average now becomes 80 kg. If another man T whose weight is 3 kg more than that of S replaces P, then the average weight Q, R, S and T becomes 79 kg. What is the weight of P?
106. A team of 8 persons joins in a shooting competition. The best marksman scored 85 points. If he had scored 92 points, the average score for the team would have been 84, the team score was?
107. A man whose bowling average is 12.4, takes 5 wickets for 26 runs and there by decreasing his average by 0.4. The number of wickets taken by him before his last match is?
108. The mean temperature of Monday to Wednesday was 370 and that from
Tuesday to Thursday was 340. If the temperature of Thursday was 45
th that of
Monday. The temperature of Thursday was?
109. 16 children are to be divided into two groups A and B of 10 and 6 children. The average percentage marks obtained by the children of group A is 75 and the average percentage of marks of all the 16 children is 76. What is the average percentage of marks of children of group B?
110. Of the three numbers the first is twice the second and the second is twice the
third. The average of the reciprocal of the numbers is772
, the numbers are?
111. The average of 5 numbers is 7, when 3 new numbers are added the average of the eight numbers is 8.5. The average of the three new numbers is?
112. The average temperature of the town in the first four days of a month was 580. The average for the second, third, fourth and fifth days was 600. If the temperature of the first and fifth days were in the ratio of 7: 8, then what is the temperature on the fifth day?
113. A football team has played 3 games so far this season. The amount of points they scored in those games is 10, 9, and 14. What is their average score for a game?
114. Ms. Smith bowls five games with scores of 200, 180, 190, 178 and 155. What was her average?
115. Betty bowled 3 games. The first 2 games her scores were 200 and 90. Her average score was 140. What did she bowl in the 3rd game?
116. Sal bought 4 DVD’s at the store. The cost of the first 3 movies was $12, $14, and $18. The average price he paid for a move was no more than $15. What was the most money he could have spent on the 4th movie?
117. Lola’s scores in two bowling games were 160 and 185. He needs an average score of at least 175 to win a championship. What is the minimum score Lola can receive in a 3rd game in order to win the championship?
118. The chart below that shows the number of students on the different teams. Find the number of students who play volley ball if the average number of student in a team is 41.
Team Number of students
Cricket 52
Football 48
Baseball 30
Volleyball
x
119. Clayton plays basketball on a team. He has played three games so far. In the first game, he scored 10 points. In the second game, he scored 14 points. In the third game, he scored 6 points. What is Clayton’s average point per game?
120. Mandy earns money by delivering groceries. She earned Rs.4 on Monday, Rs.7 on Tuesday, Rs.5 on Wednesday, Rs.4 on Thursday and Rs.5 on Friday. What is the average amount of money Mandy earned per day?
121. Jean loves to go bird watching. One day she saw 7 birds. The nest day she saw 11 birds. The next day she saw no birds. What is the average number of birds Jean saw each day?
122. Harvey read 5 books in January, 8 books in February, 4 books in March, and 7 books in April. What is the average number of books Harley read per month?
123. Carlos has three test scores of 84, 90, and 86. There is one more test during the semester. He wants to get an A+ in the class, which means she needs his average to be a minimum of 90. What score does he need to make on the fourth test to make an A+ in the class?
124. Anita has taken four tests and made 82, 77, 75, and 84. She has to take a final exam, Anita really wants to make a B grade, which means she needs an overall average of 80. What does Anita need to score in the final to get a B grade?
125. Jim has four test scores of 86, 81, 80, and 75. There is one more test during the semester. He wants to make a B grade for which means he needs his average to be an 80. What score does Jim need to make on the fifth test to make it to a B grade?
126. Janna has taken three tests and made 92, 77, and 95. She has to take a final exam, Janna really wants to make an A+ grade in the class, which means she needs an overall average of 90, what score does she need to get to make to A+ grade?
127. Find the average of all prime numbers between 30 and 50?
128. Find the average of first 40 natural numbers?
129. Find the average of first 20 multiples of 7?
130. The average of four consecutive even numbers is 27. Find the largest of these numbers?
131. There are two sections A and B of a class consisting of 36 and 44 students respectively. If the average weight of section A is 40kg and that of section B is 35kg, find the average weight of the whole class?
132. Of the three numbers, second is twice the first and is also thrice the third. If the average of the three numbers is 44. Find the largest number?
133. The average of 25 results is 18.The average of 1st 12 of them is 14 & that of last 12 is 17. Find the 13th result.
134. The Average of 11 results is 16, if the average of the 1st 6 results is 58 & that of the last 63. Find the 6th result.
135. The average weight of A, B, C is 45 Kg. The average weight of A & B is 40Kg and that of B and C is 43Kg. Find the weight of B.
136. The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by3 months. Find the age of the teacher.
137. There were 35 students in a hostel. Due to the admission of 7 new students, the expenses of the mess were increased by Rs. 42 per day while the average expenditure per head diminished by Rs 1. What was the original expenditure of the mess?
138. A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th innings.
139. Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56 km/hr, find the average speed of the train during the whole journey.
140. The average score of boys in an examination in a school is 71 and that of girls is 73. The average score of school is 71.8. The ratio of the number of the boys to girls that appeared in the examination is?
141. A train 200 metres long takes 20 seconds to cross a platform of 300 metres long. The speed of the train in metres per second is?
142. A passenger train 140 metres long travelling at a speed of 80 km/hr crosses a train 185 metres long coming from the opposite direction in 8 seconds. What is the speed of the second train?
143. A group of students were given a special test. The test was completed by various students in the following time (in minutes). Find the average time taken by the students to complete the test?
Students Time taken (in minutes)
35 18
25 20
5 15
35 12
144. The mean age of 5 children of a family is 12 years. If four of them are 6, 11, 13 and 16 years of age. Find the age of the fifth child?
145. The average of five numbers is 27. If one of the numbers is excluded, the average becomes 25. Determine the excluded number?
146. The average of 5 observations is 15. If the average of the first three observations is 14 and that of the last three is 17, find the third observation?
147. If the average marks of three groups of 8, 10 and 12 students respectively are 50, 55, 60, then find the average marks of all the students.
148. The average weight of a class of 20 students is 48 kg. Two more students weighing 60 kg 58 kg respectively join the class. What is the mean weight of the class now?
149. The average attendance of a school for the first 4 days of the week was 780 and for the first five days it was 840. How many were present on Friday?
150. The mean of 6 numbers is 32. If one of the number is excluded, the mean reduces by 2. The excluded number is?
