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Average (Practice Sheet)

 Practice Material : 

Q 1. Find the average of all numbers between 5 and 49 which are divisible by 5.

  1. 20

  2. 25

  3. 30

  4. 35

Sol : No. divisible by 5 between 5 and 49 = 5, 10, 15, 20, 25, 30, 35, 40, 45

        No. of observations  = 9 (ODD)

        The Average of Odd no. of Observation in consecutive pattern  = MIDDLE TERM

        Average of the No. divisible by 5 between 5 and 49 =  25


2. The sum of four consecutive even numbers is 36 . Find the largest of these numbers.

  1. 8

  2. 10

  3. 12

  4. 14

Sol : Let the number numbers be X, X+2 , X+4 , X+6

        According to question,

        X + X+2 + X+4 + X+6 = 36

                              4X + 12 = 36

                                     4X  = 24

                                       X  = 6 

        Largest of these number = X + 6 =  6 + 6 = 12


Q 3. The average of 11 numbers is 30. If the average of first six numbers is 17.5 and that of last six is 42.5, then what is the sixth number ?

  1. 30

  2. 36

  3. 45

  4. 47

Sol : Average of 11 numbers = 30

        Sum of 11 numbers = 30 x 11 = 330

        Average of First six numbers = 17.5

       Sum of First six numbers = 17.5 x 6 = 105

       Average of Last six numbers = 42.5

       Sum of Last six numbers = 255

       Hence, Sixth Number = (255 + 105) - 330 = 360 - 330 = 30


Q4. The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero ?

  1. 0

  2. 1

  3. 10

  4. 19

Sol : Average of 20 numbers = 0

        Sum of the 20 numbers = 0

        If sum of 19 numbers = k

        And 20th number = -k

       Sum of the 20 numbers = 0

       Hence, at the most, 19 terms are positive. i.e. greater than zero.


Q 5.  The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?

  1. 76 kg

  2. 76.5 kg

  3. 85 kg

  4. Data Inadequate

  5. None of these

Sol : Increase in average = 2.5 Kg

        Sum of the increased average = 2.5 x 8 = 20 kg

        Hence, Weight of the new person = 20 + 65 = 85 kg


Q 6. The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:

  1. 3500

  2. 4000

  3. 4050

  4. 5000

Sol : Average monthly income of P and Q = Rs. 5050

        Sum of the monthly income of P and Q = 5050 x 2 = 10100

        Average monthly income of Q and R = Rs. 6250

       Sum of the monthly income of Q and R = 6250 x 2 = 12500

        Average monthly income of P and R = Rs. 5200

       Sum of the monthly income of P and R = 5200 x 2 = 10400

       On adding all the sum of monthly income of P, Q and R ; we get

                   2 (P + Q + R ) = 33000

                     P + Q + R     = 16500

       Monthly income of P =  (P + Q + R ) - (Q + R) = 16500 - 12500

       Hence, monthly income of P = Rs. 4000

     

Q 7. The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:     

  1. 35 years

  2. 40 years

  3. 45 years

  4. 50 years

Sol : Average age of husband, wife and their child 3 years ago = 27 years

        Sum Of the age of husband, wife and their child 3 years ago = 27 x 3 = 81 years

       Sum of the present age of husband, wife and their child  = 81 + 3 x 3 = 81 + 9 = 90 years

        Average age of wife and child (5 years ago) = 20 years

        Sum of the age of wife and child (5 years ago) = 20 x 2 = 40 years

        Sum of the present age of wife and child = 40 + 2 x 5 = 40 + 10 = 50 years

        Hence, Present age of husband = 90 - 50 = 40 years 


Q 8. The average marks of a Suresh in 10 papers are 80. If the highest and the lowest scores are not considered, the average is 81. If his highest score is 92, find the lowest?

  1. 55

  2. 60

  3. 62

  4. Can’t be determined

Sol : Average marks of a Suresh in 10 papers = 80  

       Sum of the marks of a Suresh in 10 papers = 80 x 10 = 800

       Average marks of a Suresh in 8 papers = 81       {Excluding the Highest and the Lowest }

       Sum of the marks of a Suresh in 8 papers = 81 x 8 = 648

       Sum of highest and lowest marks = 800 - 648 = 152

       Lowest Marks = 152 - 92 = 60

      Hence the lowest marks = 60 


Q 9. The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:

  1. 17 Kg  

  2. 20 Kg

  3. 26 Kg

  4. 31 Kg

Sol :  Average weight of A, B and C = 45 kg

         Sum of the weight of A, B and C = 45 x 3 = 135 Kg

         Average weight of A and B = 40 kg

         Sum of the weight of A and B = 40 x 2 = 80 Kg

         Average weight of B and C = 43 kg

         Sum of the weight of B and C = 43 x 2 = 86 Kg

         Weight of C = (A + B + C ) - (A + B) = 135 - 80 = 55 Kg

        Hence, the  Weight of B = (B + C) - C = 86 - 55 = 31 Kg


Q 10. . The average of the 9 consecutive positive integers is 63. The product of the largest and smallest integer is :

  1. 3935

  2. 3953

  3. 3853

  4. 3845

Sol : Let the integers be 

          X, (x+1) , (X + 2), (X + 3), (X + 4), (X + 5, (X + 6), (X + 7), (X + 8)

 According to question , 

Average = 63 = (X + 4)

 Smallest Integer,   X = 59

 Largest Integer , (X + 8) = 59 + 8 = 67

Hence the required answer is = 59 x 67  = 3953


Q 11. The average of 65 numbers is 137.5. The average of first 32 numbers is 132.6 and that of last 32 numbers is 140.5. Find the 33rd number ?

  1. 159

  2. 207.5

  3. 198

  4. 186.5

Sol : Average of 65 numbers = 137.5

        Sum of the 65 observations = 137.5 x 65 = 8937.5

        Average of first 32 numbers = 132.6

        Sum of the first 32 observations = 132.6 x 32 = 4243.5

        Average of last 32 numbers = 140.5

       Sum of the last 32 observations = 32 x 140.5 = 4496

       Sum of all 64 numbers = 8739.5

       Hence the 33rd Observation = 8937.5 - 8739.5 = 198


Q 12. The average weight of the boys in a class is 69.3 kg and that of the girls in the same class is 59.4. If the average weight of all the boys and girls in the class is 63.8 kg, then the percentage of the number of boys in the class :

  1. 44 4/9

  2. 55 5/9

  3. 45

  4. 40

Sol : Average weight of the boys in a class = 69.3 kg

        Average weight of girls in the same class =  59.4 kg

        Average weight of all the boys and girls in the class = 63.8 kg

        

                                       W₁X₁ + W₂X₂ + W₃X₃

Weighted Average  =  ━━━━━━━━━━━━

                                          W₁ + W₂ + W₃

         

        Let the no. of girls be G and boys be B in the class

According to question,

                63.8 (B + G) = 69.3 B + 59.4 G

                        4.4 G    =     5.5 B

                         G / B   =    5 / 4 

 Hence , percentage of boys in the class = (4 / 9 ) x 100 = 44 4/9%


Q 13. The average age of 4 brothers is 15 years. If their father’s age is included, the average is increased by 5 years. The age of the father (in years) :

  1. 35 years

  2. 40 years

  3. 38 years

  4. 36 years

Sol : Average age of 4 brothers = 15 years

       Sum of the ages of 4 brothers = 15 x 4 = 60 years

       When father’s age is also included, average increases by 5

       New average = 20 years

       Sum of the ages of father and sons = 5 x 20 = 100 years

      Hence,  the age of Father = 100 - 60 = 40 years


Q14. The average age of the family of five members is 24 years. If the present age of the youngest is 8 years, what was the average age of the family at the time of birth of the youngest member ?

  1. 16

  2. 20

  3. 24

  4. 18

Sol : Average age of the family of five members = 24 years

        Sum of the age of the family of five members =  24 x 5 = 120  years

        Sum of the ages of the family at the time of birth of the youngest member = 120 - (8 x 5) 

                                                                                                                              = 80 years

        Average  age of the family at the time of birth of the youngest member = 80 / 4 = 20 years

        Hence the average age of the family at the time of birth of the youngest member is 20 years. 


Q 15. The average age of 21 members of a family is 32 years. If two persons each have age 56 years, left the group and one more person 20 years old left, then find the average age of remaining persons.

  1. 25

  2. 27

  3. 30

  4. 29

Sol :  Average age of 21 members of a family = 32 years

         Sum of the  age of 21 members of a family = 32 x 21 = 672 years

         Sum of the ages who left the group = 2 x 56 + 20 = 132 years 

         Sum of the age of remaining members = 540 years

         Hence, Average age of remaining members = 540 / 18 = 30 years

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