Average Weight and Salary Problems
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What is the total weight of the seven students who left the class?

  • 300 kg
  • 240 kg
  • 280 kg (correct)
  • 280 kg (correct)

    • What is the total initial weight of the 49 students in the class?

  • 1911 kg (correct)
  • 2100 kg
  • 1728 kg
  • 2056 kg

    • If the average weight of the new students joining the class is 54 kg, what is their total weight?

  • 378 kg (correct)
  • 504 kg
  • 336 kg
  • 420 kg

    • After the changes, how many students are there in the class?

    <p>50</p> Signup and view all the answers

    What is the new average weight of the class after the changes?

    <p>41 kg</p> Signup and view all the answers

    What is the average weight of the remaining students after the seven leave?

    <p>40 kg</p> Signup and view all the answers

    What is the average salary of workers in the company?

    <p>Rs. 54,000</p> Signup and view all the answers

    What is the average salary of an officer based on the details given?

    <p>Rs. 1,20,000</p> Signup and view all the answers

    How much did the 20th student spend, if the average of all 20 students was Rs. X?

    <p>Rs. 193</p> Signup and view all the answers

    If 19 students spent Rs. 175 each, what was the total amount they spent?

    <p>Rs. 3,325</p> Signup and view all the answers

    What is the 8th result if the average of the first 7 results is 21 and the average of the last 7 results is 20, with an overall average of 21 for 15 results?

    <p>40 years</p> Signup and view all the answers

    In a class of 45 students with 20 girls scoring an average of 42 marks, what are the average marks of the boys if the overall class average is 36?

    <p>28</p> Signup and view all the answers

    If the average temperature for four days is 600, what is the temperature of Friday if the average for the next four days is 630 and the ratio of temperatures between Monday and Friday is 21:25?

    <p>31.20</p> Signup and view all the answers

    What score does Sunil need in his 17th inning to raise his average from 37 to 46?

    <p>780</p> Signup and view all the answers

    What is the average age of all the girls in a class if 25 girls have an average age of 11.2 years and 15 other girls have an average age of 10 years?

    <p>167 years</p> Signup and view all the answers

    Given the averages of a set of scores, how can we determine the single outlier score that affects the average significantly?

    <p>By calculating the mean of the remaining scores</p> Signup and view all the answers

    In a test scoring setup, how does increasing the score of a single student impact the class's average?

    <p>Increases the average if the individual score is above the current average</p> Signup and view all the answers

    If the average score of a group increases, what can we infer about the scores of at least some members of that group?

    <p>At least one score must have increased</p> Signup and view all the answers

    How would you calculate the new average if a consistent number of participants consistently score below the overall average?

    <p>Consider the scores of all participants equally</p> Signup and view all the answers

    If the total average score of a class is 36, but half of the students score below 36, what can be said about the other half?

    <p>Some may score at or below 36</p> Signup and view all the answers

    What is the average age of all the girls in the class based on the given information?

    <p>11.35 years</p> Signup and view all the answers

    If X : Y = 3 : 5, what is the value of A + X + Y based on the given ratios?

    <p>2012</p> Signup and view all the answers

    What was the incorrect weight entered for a person and how did it affect the average weight?

    <p>83 kg increased average by 500 gm</p> Signup and view all the answers

    What is the weight of player B based on the average weights of A, B, and C?

    <p>48 kg</p> Signup and view all the answers

    How many total people are in the group if the average weight increased by 500 gm?

    <p>80</p> Signup and view all the answers

    In the context of the age average, what is the implication of combining groups with different averages?

    <p>The new average can be lower than both groups.</p> Signup and view all the answers

    If the average of A, B, and C is 65 kg and the average of A and B is 62 kg, what can be inferred about the weights?

    <p>A must weigh less than C.</p> Signup and view all the answers

    If the total marks of the group of 10 students is X, what is the meaning of the ratio X : Y = 3 : 5?

    <p>X is less than Y but could be equal to other ratios.</p> Signup and view all the answers

    What is necessary to calculate the average properly when weights are incorrectly recorded?

    <p>The correct weights and the number of entries.</p> Signup and view all the answers

    What impact does an erroneous entry have on averages in a dataset?

    <p>It can skew the averages depending on group size.</p> Signup and view all the answers

    What is the average weekly income of the shopkeeper in February 2021?

    <p>Rs. 21,980</p> Signup and view all the answers

    What is the average daily income of the shopkeeper in February 2021 assuming it has 28 days?

    <p>Rs. 3,227</p> Signup and view all the answers

    If 40% of the total 50 students are girls, how many boys are there?

    <p>30 boys</p> Signup and view all the answers

    What percentage less is the average score of the boys compared to the girls?

    <p>20%</p> Signup and view all the answers

    What is the average score of the boys if the average score of all students is 66?

    <p>58</p> Signup and view all the answers

    What happens to the average weight of 8 men when one weighing 65 kg is replaced?

    <p>It increases by 1.5 kg</p> Signup and view all the answers

    What is the weight of the new man who replaces the one weighing 65 kg?

    <p>80 kg</p> Signup and view all the answers

    What does the average weight of 18 persons become when one person weighing 72 kg is replaced?

    <p>It increases by 2.5 kg</p> Signup and view all the answers

    If the average score of the girls is 36 and boys have an average of 26, what is the overall score needed to maintain an average of 30?

    <p>30</p> Signup and view all the answers

    How many girls must have appeared for the test if there are 15 boys with an average score of 26?

    <p>8 girls</p> Signup and view all the answers

    If the average weight of 18 individuals increases by 2.5 kg when a new person replaces one weighing 72 kg, what is the weight of the new individual?

    <p>117 kg</p> Signup and view all the answers

    Calculate the average monthly income of a family during the year if their average expenditures were Rs. 13,750 for the first four months, Rs. 11,750 for the next three months, and Rs. 31,750 for the last five months, with total savings of Rs. 15,550.

    <p>Rs. 4,00,000</p> Signup and view all the answers

    In a class with 29 boys and 21 girls, if the average score of boys in Maths is 89 and the average score of girls is 91, what is the overall average score of the class?

    <p>89.84</p> Signup and view all the answers

    If a worker's average income for a week is Rs. 180 and he earned Rs. 115, Rs. 212, Rs. 170, Rs. 165, Rs. 185, and Rs. 225 from Monday to Saturday, how much did he earn on Sunday?

    <p>Rs. 95</p> Signup and view all the answers

    What is the total weight of the 18 individuals before the new individual is added if the average weight with the new person included is higher by 2.5 kg?

    <p>1270 kg</p> Signup and view all the answers

    During the whole year, the average monthly expenditure of a family was defined at three different periods. If the total expenditure summary is Rs. 69,750, what is the total annual income including the savings?

    <p>Rs. 4,25,000</p> Signup and view all the answers

    Which of the following statements correctly interprets the change in average weight when a 72 kg individual is replaced by someone else?

    <p>The new person's weight increases the total average weight.</p> Signup and view all the answers

    When calculating average scores in a mixed-gender class, which of the following is essential?

    <p>Total combined scores of all students</p> Signup and view all the answers

    If a family's average expenditure increases significantly in the last months of the year, what could be a likely impact on their overall savings?

    <p>Decreased savings if income does not increase.</p> Signup and view all the answers

    If the average weight of an individual is known and a new person increases the average, what inference can be made about the new individual?

    <p>Their weight must be exceeding the previous average.</p> Signup and view all the answers

    Study Notes

    Average Weight Problems

    • In a class of 49 students, the average weight is 39 kg.
    • Seven students with an average weight of 40 kg leave the class.
    • Seven new students with an average weight of 54 kg join the class.
    • The total weight of the initial 49 students is 49 * 39 = 1911 kg.
    • The total weight of the seven students leaving is 7 * 40 = 280 kg.
    • The total weight of the seven students joining is 7 * 54 = 378 kg.
    • The total weight of the class now is 1911 - 280 + 378 = 2009 kg.
    • The new average weight of the class is 2009 / 49 = 41 kg.

    Average Salary Problems

    • In a company, there are workers and officers.
    • The average monthly salary of an officer is Rs. 78,000 more than the combined average monthly salary of an employee.
    • The combined average monthly salary of an employee is Rs. 42,000 more than the average monthly salary of a worker.
    • Let the average monthly salary of a worker be x.
    • The combined average monthly salary of an employee is x + 42,000.
    • The average monthly salary of an officer is (x + 42,000) + 78,000 = x + 120,000.
    • The percentage of officers in the company is not provided in the given text. Therefore, it cannot be determined.

    Average Age Problems

    • There are 25 girls in a class with an average age of 11.2 years.
    • There are 15 more girls with an average age of 10 years.
    • The total age of the first 25 girls is 25 * 11.2 = 280 years.
    • The total age of the remaining 15 girls is 15 * 10 = 150 years.
    • The total age of all 40 girls is 280 + 150 = 430 years.
    • The average age of all 40 girls is 430 / 40 = 10.75 years.

    Average Marks Problems

    • In a class of 45 students, 20 girls scored an average of 42 marks in a test of 50 marks.
    • The class average is 36 marks.
    • The total marks of the 20 girls is 20 * 42 = 840 marks.
    • The total marks of the entire class is 45 * 36 = 1620 marks.
    • The total marks of the boys is 1620 - 840 = 780 marks.
    • The average marks of the boys is 780 / 25 = 31.20 marks.

    Average of Consecutive Natural Numbers

    • The average of the first 43 natural numbers is the same as the average of the first and last number in the sequence.
    • The average of the first 43 natural numbers is (1+43)/2 = 22.

    Finding Missing Number

    • There are 15 numbers with an average of 21.
    • The first seven numbers have an average of 21.
    • The last seven numbers have an average of 20.
    • The sum of the first seven numbers is 7 * 21 = 147.
    • The sum of the last seven numbers is 7 * 20 = 140.
    • The total sum of all the numbers is 15 * 21 = 315.
    • The eighth number is therefore, 315 - 147 - 140 = 28.

    Average Score in a Test

    • In a test, 50 students have an average score of 66.
    • 40% of the students are girls, which is 50 * 0.4 = 20 girls.
    • This leaves 50 - 20 = 30 boys.
    • The total score for all students is 50 * 66 = 3300.
    • The average score of the boys is 20% less than the average score of the girls.
    • Let the girls' average score be x, then the boys' average score is 0.8x.
    • Using the formula (Total Score) = (Number of students * Average Score) for both boys and girls:
      • 20x + 30(0.8x) = 3300
      • 20x + 24x = 3300
      • 44x = 3300
      • x = 75 (Average score of the girls)

    Average Weight with Replacement

    • 8 men have an average weight that is increased by 1.5 kg when one man weighing 65 kg is replaced.
    • The total weight of the 8 original men is 8 * (original average weight)
    • The total weight increases by 8 * 1.5 = 12 kg.
    • Therefore, the weight of the new man is 65 + 12 = 77 kg.

    Increasing Average Score

    • Sunil's average score over 17 innings is 37 runs.
    • He wants to increase his average by 9 runs.
    • His new target average is 37 + 9 = 46 runs.
    • His total score over 17 innings should be 17 * 46 = 782 runs.
    • To achieve this, he needs to score 782 - (16 * 37) = 108 runs in his 17th innings.

    Average Weight of Three People

    • The average weight of A, B, and C is 65 kg, meaning their total weight is 3 * 65 = 195 kg.
    • The average weight of A and B is 62 kg, meaning their total weight is 2 * 62 = 124 kg.
    • The average weight of B and C is 66 kg, meaning their total weight is 2 * 66 = 132 kg.
    • To find B's weight, we can add the total weights of A and B and B and C, and then subtract the total weight of A, B, and C: [(124 + 132) - 195] = 59 kg.
    • B's weight is therefore 59 kg.

    Average Income for February

    • A shopkeeper has weekly earnings in February 2021: Rs. 21,980, Rs. 20,580, Rs. 22,380, Rs. 22,616.
    • February has 28 days.
    • The total earnings for February are 21,980 + 20,580 + 22,380 + 22,616 = Rs. 87,556.
    • The average daily income is Rs. 87,556 / 28 = Rs. 3,127.

    Counting Girls in a Test

    • 15 boys scored an average of 26 in a test, totaling 15 * 26 = 390 marks.
    • The combined average score for boys and girls is 30.
    • Assuming there are "x" girls, the total score of all participants is (15 + x) * 30 = 450 + 30x.
    • The girls scored an average of 36, contributing a total of 36x marks.
    • Combining the scores of boys and girls: 390 + 36x = 450 + 30x
    • Solving for 'x': 6x = 60
    • Therefore, there were 60 / 6 = 10 girls in the test.

    Class Average in Maths

    • There are 29 boys with an average score of 89 in Maths, totaling 29 * 89 = 2581 marks.
    • There are 21 girls with an average score of 91 in Maths, totaling 21 * 91 = 1911 marks.
    • The total marks of the class in Maths are 2581 + 1911 = 4492.
    • The average score for the whole class is 4492 / (29 + 21) = 4492 / 50 = 89.84.

    Weekly Income Calculation

    • A worker earns Rs. 180 on average per week.
    • He earns Rs. 115, Rs. 212, Rs. 170, Rs. 165, Rs. 185, and Rs. 225 from Monday to Saturday, totaling Rs. 1072.
    • To reach his average weekly income, he must earn Rs. 180 * 7 = Rs. 1260 for the week.
    • Therefore, his Sunday's income is Rs. 1260 - Rs. 1072 = Rs. 188.

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    Description

    This quiz explores problems related to calculating averages in two contexts: weight among students and salaries in a company. It focuses on understanding how averages change with the addition and removal of groups. Test your skills in handling average problems with this comprehensive set of questions.

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