Average Problems and Solutions

• 1. Average of 10 matches is 32, How many runs one should should score to increase his average by 4 runs.

  1. 70
  2. 76
  3. 78
  4. 80

  Answer :

  Option B

  Explanation:

  Average after 11 innings should be 36
  
  So, Required score = (11 * 36) - (10 * 32)
  = 396 - 320 = 76

• 2. The average age of the mother and her six children is 12 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother

  1. 40
  2. 41
  3. 42
  4. 43

  Answer :

  Option C

• 3. Find the average of first 10 multiples of 7

  1. 35.5
  2. 37.5
  3. 38.5
  4. 40.5

  Answer :

  Option C

  Explanation:

  \begin{aligned}
  = \frac {7(1+2+3+...+10)}{10}
  \end{aligned}
  
  \begin{aligned}
  = \frac {7(10(10+1))}{10 \times 2}
  \end{aligned}
  
  \begin{aligned}
  = \frac {7(110)}{10 \times 2} = 38.5
  \end{aligned}

• 4. Find the sum of first 30 natural numbers

  1. 470
  2. 468
  3. 465
  4. 463

  Answer :

  Option C

  Explanation:

  Sum of n natural numbers
  \begin{aligned}
  = \frac{n(n+1)}{2}
  \end{aligned}
  
  \begin{aligned}
  = \frac{30(30+1)}{2} = \frac{30(31)}{2} = 465
  \end{aligned}

• 5. Average of all prime numbers between 30 to 50

  1. 37
  2. 37.8
  3. 39
  4. 39.8

  Answer :

  Option D

  Explanation:

  Prime numbers between 30 and 50 are:
  31, 37, 41, 43, 47
  
  Average of prime numbers between 30 to 50 will be
  \begin{aligned}
  (\frac{31+37+41+43+47}{5}) = \frac{199}{5} = 39.8
  \end{aligned}

• 6. Find the average of all numbers between 6 and 34 which are divisible by 5

  1. 15
  2. 20
  3. 25
  4. 30

  Answer :

  Option B

  Explanation:

  \begin{aligned}
  Average = (\frac{10+15+20+25+30}{5}) = \frac{100}{5} =20
  \end{aligned}

• 7. Average of first five multiples of 3 is

  1. 9
  2. 11
  3. 13
  4. 15

  Answer :

  Option A

  Explanation:

  \begin{aligned}
  Average = \frac{3(1+2+3+4+5)}{5} = \frac{45}{5} = 9
  \end{aligned}