Average Problems and Solutions

• 8. The average of four consecutive odd numbers is 24. Find the largest number.

  1. 25
  2. 27
  3. 29
  4. 31

  Answer :

  Option B

  Explanation:

  Let the numbers are x, x+2, x+4, x+6, then
  \begin{aligned}
  => \frac{x+(x+2)+(x+4)+(x+6)}{4} = 24
  \end{aligned}
  
  \begin{aligned}
  => \frac{4x+12)}{4} = 24
  \end{aligned}
  
  \begin{aligned}
  => x+3 = 24 => x = 21
  \end{aligned}
  
  So largest number is 21 + 6 = 27

• 9. Average weight of 10 people increased by 1.5 kg when one person of 45 kg is replaced by a new man. Then weight of the new man is

  1. 50
  2. 55
  3. 60
  4. 65

  Answer :

  Option C

  Explanation:

  Total weight increased is 1.5 * 10 = 15.
  So weight of new person is 45+15 = 60

• 10. 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

  1. 54.48
  2. 54.68
  3. 54.60
  4. 54.58

  Answer :

  Option B

  Explanation:

  \begin{aligned}
  \frac{(55 \times 50) +(60 \times 55) +(45 \times 60) }{55 + 60 + 45}
  \end{aligned}
  
  \begin{aligned}
  \frac{8750}{160} = 54.68
  \end{aligned}

• 11. The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is

  1. 45
  2. 50
  3. 55
  4. 60

  Answer :

  Option A

• 12. When a student weighing 45 kgs left a class, the average weight of the remaining 59 students increased by 200g. What is the average weight of the remaining 59 students

  1. 55
  2. 56
  3. 57
  4. 58

  Answer :

  Option C

  Explanation:

  Let the average weight of the 59 students be A.
  So the total weight of the 59 of them will be 59*A.
  
  The questions states that when the weight of this student who left is added, the total weight of the class = 59A + 45
  When this student is also included, the average weight decreases by 0.2 kgs
  
  \begin{aligned}
  \frac{59A + 45}{60} = A - 0.2
  \end{aligned}
  
  => 59A + 45 = 60A - 12
  => 45 + 12 = 60A - 59A
  => A = 57

• 13. Average age of boys in a class is 16 years and average age of girls is 15 years, what is the average age of all

  1. 15.5
  2. 15
  3. 16
  4. Cant be computed

  Answer :

  Option D

  Explanation:

  As number of girls and boys is not given so result cant be computed

• 14. Reeya obtained 65, 67, 76, 82 and 85 out of 100 in different subjects, What will be the average.

  1. 70
  2. 75
  3. 80
  4. 85

  Answer :

  Option B

  Explanation:

  \begin{aligned}
  ( \frac {65+67+76+82+85}{5} ) = 75
  \end{aligned}