Average Weight and Salary Problems

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.