##### Average: Aptitude questions and answers

Average concepts are crucial and fundamental for students in order to solve questions properly.

• In mathematics, Average is defined as the mean value, which is equal to the ratio of the sum of all values in a set to the total number of values/units present in the set.
• The data can be anything like age, money, runs, etc. Average has many applications in real-life.

1] The average of 10 numbers is 15. If one number is removed and the average becomes 16, what is the value of the number that was removed?

 To solve this, we can use the concept of averages. The sum of the 10 numbers is 10 multiplied by the average (15), which equals 150. Now, if one number is removed, the sum of the remaining 9 numbers is 9 multiplied by the new average (16), which equals 144. The number that was removed is the difference between the original sum (150) and the sum of the remaining numbers (144), which is 6. Answer: The value of the removed number is 6.

2] The average height of 30 students in a class is 150 cm. If the teacher’s height is included, which is 170 cm, what is the new average height?

 Calculate the sum of the heights of the 30 students by multiplying the average height (150 cm) by the number of students: 150 cm * 30 = 4500 cm. Add the teacher’s height (170 cm) to the sum of the students’ heights: 4500 cm + 170 cm = 4670 cm. Determine the new average by dividing the updated total height (4670 cm) by the total number of people (30 students + 1 teacher = 31): 4670 cm / 31 = 150.65 cm (rounded to two decimal places). Answer: The new average height, when the teacher’s height is included, is approximately 150.65 cm.

3] The average weight of 6 students is 50 kg. If a student with a weight of 60 kg joins the group, what is the new average weight?

 To find the new average weight when a student with a weight of 60 kg joins the group, follow these steps: The average weight of the initial 6 students is 50 kg. This means that the total weight of these 6 students is 6 multiplied by the average, which is 6 * 50 = 300 kg. When a student with a weight of 60 kg joins the group, we add their weight to the total weight of the initial 6 students. The new total weight becomes 300 kg + 60 kg = 360 kg. Determine the new average weight by dividing the updated total weight (360 kg) by the new total number of students (6 initial students + 1 new student = 7): 360 kg / 7 = 51.43 kg (rounded to two decimal places). Answer: The new average weight, when a student with a weight of 60 kg joins the group, is approximately 51.43 kg.

4] The average weight of a group of 8 friends is 65 kg. If the weight of one friend is mistakenly recorded as 70 kg instead of 50 kg, what is the correct average weight?

 To find the correct average weight after correcting the mistaken recording, follow these steps: The average weight of the group of 8 friends is 65 kg. This means that the total weight of these 8 friends is 8 multiplied by the average, which is 8 * 65 = 520 kg. One friend’s weight is mistakenly recorded as 70 kg instead of the correct weight of 50 kg. To correct this, we need to adjust the total weight by subtracting the excess weight recorded for that friend and adding the correct weight. Subtract the excess weight: 520 kg – 70 kg = 450 kg. Add the correct weight: 450 kg + 50 kg = 500 kg. Determine the correct average weight by dividing the updated total weight (500 kg) by the total number of friends (8): 500 kg / 8 = 62.5 kg. Answer: The correct average weight, after correcting the mistaken recording, is 62.5 kg.

5] The average age of a family of four members is 30 years. If the average age of the parents is 35 years and the average age of the children is 20 years, how old is the fourth family member?

 To find the age of the fourth family member, we need to use the concept of averages and consider the given information: The average age of the family of four members is 30 years. This means that the sum of the ages of the four family members is 4 multiplied by the average, which is 4 * 30 = 120 years. We are given that the average age of the parents is 35 years. This implies that the sum of the parents’ ages is 2 multiplied by the average age of the parents, which is 2 * 35 = 70 years. We are also given that the average age of the children is 20 years. This means that the sum of the children’s ages is 2 multiplied by the average age of the children, which is 2 * 20 = 40 years. To find the age of the fourth family member, we subtract the sum of the parents’ ages and the sum of the children’s ages from the sum of the ages of all four family members: Fourth family member’s age = Sum of all four family members’ ages – Sum of parents’ ages – Sum of children’s ages = 120 years – 70 years – 40 years = 10 years. Answer: The fourth family member is 10 years old.

6] The average of six numbers is 18. If two numbers are 12 and 20, what is the average of the remaining four numbers?

 To find the average of the remaining four numbers, given that the average of six numbers is 18 and two numbers are 12 and 20, follow these steps: The average of the six numbers is 18. This means that the sum of the six numbers is 6 multiplied by the average, which is 6 * 18 = 108. We are given that two numbers are 12 and 20. To find the sum of the remaining four numbers, subtract the sum of these two numbers from the total sum of the six numbers: Sum of remaining four numbers = Sum of six numbers – Sum of two given numbers = 108 – (12 + 20) = 108 – 32 = 76. To find the average of the remaining four numbers, divide the sum of the remaining four numbers by 4 (the total number of remaining numbers): Average of remaining four numbers = Sum of remaining four numbers / 4 = 76 / 4 = 19. Answer: The average of the remaining four numbers is 19.

7] The average of three numbers is 25. If two of the numbers are 20 and 30, what is the third number?

 To find the third number, given that the average of three numbers is 25 and two of the numbers are 20 and 30, follow these steps: 1. The average of the three numbers is 25. This means that the sum of the three numbers is 3 multiplied by the average, which is 3 * 25 = 75. 2. We are given that two of the numbers are 20 and 30. To find the third number, subtract the sum of these two numbers from the total sum of the three numbers: Third number = Sum of three numbers – Sum of two given numbers = 75 – (20 + 30) = 75 – 50 = 25. Answer: The third number is 25.

8] The average salary of 12 employees in a company is \$4,000. If the CEO’s salary is added, which is \$100,000, what is the new average salary?

 To find the new average salary when the CEO’s salary is added, follow these steps: 1. The average salary of 12 employees is \$4,000. This means that the total salary of the 12 employees is 12 multiplied by the average, which is 12 * \$4,000 = \$48,000. 2. The CEO’s salary is \$100,000. To find the new total salary when the CEO’s salary is added, we add the CEO’s salary to the total salary of the 12 employees: \$48,000 + \$100,000 = \$148,000. 3. Determine the new average salary by dividing the updated total salary (\$148,000) by the new total number of employees (12 employees + 1 CEO = 13): \$148,000 / 13 = \$11,384.62 (rounded to two decimal places). Answer: The new average salary, when the CEO’s salary is added, is approximately \$11,384.62.

9] The average of a group of friends’ ages is 25 years. If two friends, aged 20 and 30, join the group, what is the new average age?

Answer: (25n + 50) / (n + 2) years.

 To find the new average age when two friends, aged 20 and 30, join the group, follow these steps: 1. The average age of the group of friends is 25 years. This means that the sum of the ages of the friends in the original group is the average age multiplied by the number of friends. 2. Let’s denote the number of friends in the original group as “n”. Therefore, the sum of their ages is 25n years. 3. Two friends, aged 20 and 30, join the group. To find the new total sum of ages, we need to add the ages of these two friends to the previous sum. New total sum of ages = (Sum of ages of original group) + 20 + 30 = 25n + 20 + 30 = 25n + 50. 4. The total number of friends in the new group is the original number of friends plus the two friends who joined, which is n + 2. 5. To find the new average age, divide the new total sum of ages by the new total number of friends: New average age = (New total sum of ages) / (New total number of friends) = (25n + 50) / (n + 2). Answer: The new average age, when two friends aged 20 and 30 join the group, is (25n + 50) / (n + 2) years.

10] The average of seven numbers is 21. If one number is added, the new average becomes 22. What is the added number?

29

 To find the added number when the average of seven numbers is 21 and the new average becomes 22 after adding one number, follow these steps: 1. The average of the seven numbers is 21. This means that the sum of the seven numbers is 7 multiplied by the average, which is 7 * 21 = 147. 2. When one number is added, the new average becomes 22. To find the new sum of the numbers, multiply the new average by the total number of elements: New sum of the numbers = 22 * 8 = 176. 3. The added number can be determined by finding the difference between the new sum of the numbers and the sum of the initial seven numbers: Added number = New sum of the numbers – Sum of the initial seven numbers = 176 – 147 = 29. Answer: The added number is 29.

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