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21. The average of 3 numbers is 7, that of the first two is 4, find the third number.
  A.  17
  B.  13
  C.  15
  D.  11
     
   
View Answer

Using shortcut, we get Average of remaining students =
3x7 - 2x4 / 3 - 2
= 13

22. The average age of 24 boys and a class teacher of a class is equal to 15 years. If class teacher left the class due to health problem the average becomes 14. Find the age of class teacher who left the class.
  A.  39 years
  B.  35 years
  C.  42 years
  D.  33 years
     
   
View Answer

Shortcut: If the average of 'z' quantities is equal to 'a'. When a quantity is removed the average becomes 'b'. Then the value of the removed quantity is [z(a-b)+b] Here, z=24, a=15 b=14 Using these values in shortcut, we get [24(15-14)+14] = 25+14 = 39 Hence the age of class teacher is 39 years.

23. The total age of 26 persons are 442 years. Out of these persons one is a teacher and others are students. If the teacher's age is excluded, the average reduces by 2 years. What is the age of the teacher?
  A.  71 years
  B.  63 years
  C.  69 years
  D.  67 years
     
   
View Answer

Using shortcut, [z(a-b)+b] z=26, a=442/26=17, b=17-2=15 putting these values in shortcut, we get Age of teacher = [26(17-15) + 15] = [26x2 + 15] = 67 years

24. The average of 11 numbers is 21. if 3 is added to each given number, what will be the new average?
  A.  27
  B.  22
  C.  24
  D.  29
     
   
View Answer

Shortcut: If the average of 'z' numbers is 'a' and if 'y' is added to or subtracted from each given number, the average of 'z' numbers becomes (a+y) or (a-y) respectively. in the oher words average value will be increased or decreased by 'y' Using the shortcut, we get New average = 21 +3 = 24

25. The average of 6 numbers is 15. if 3 is subtracted from each given number, what will be the new average?
  A.  15
  B.  12
  C.  9
  D.  13
     
   
View Answer

Using the shortcut (a-y), we get New average = 15 - 3 = 12

26. The average age of 30 boys of a class is equal to 14 years. When the age of the class teacher is included the average becomes 15 years. Find the age of the class teacher.
  A.  51 yrs
  B.  43 yrs
  C.  45 yrs
  D.  49 yrs
     
   
View Answer

Shortcut: If the average of n quantities is equal to 'a' and when a new quantity is added the average becomes 'b'. Then the value of the new quantity is [n(b-a + b] here, n=30, a=14, b=15 Using these values in shortcut, we get [30(15-14)+15] = 30+15 = 45 Hence, the age of class teacher is 45 years.

27 The average of 12 numbers is 35. If each of the numbers is multiplied by 2, find the average of new set of numbers.
  A.  75
  B.  68
  C.  72
  D.  70
     
   
View Answer

Shortcut: If the average of 'n' numbers is 'a' and if each given number is multiplied to or divided by 'b', then the avergage of n numbers becomes axb or
a / b
respectively. here, n = 12, a=35, b=2 Using these values in shortcut, we get: Average = 35 x 2 = 70

28. The average of 12 numbers is 35. If each of the numbers is divided by 5, find the average of new set of numbers.
  A.  11
  B.  7
  C.  5
  D.  9
     
   
View Answer

Shortcut: If the average of 'n' numbers is 'a' and if each given number is multiplied to or divided by 'b', then the average of n numbers becomes axb or
a / b
respectively. here, n = 12, a=35, b=5 Using these values in shortcut, we get: Average =
35 / 5
= 7

29. The average weight of 4 men is increased by 3 kg when one off them who weighs 120 kg is replaced by another man. What is the weight of the new man?
  A.  132kg
  B.  125kg
  C.  135kg
  D.  137kg
     
   
View Answer

Shortcut: The average weight of 'n' persons is increased by 'a' kg when some of them who weight 'b' kg are replaced by the same number of persons. Then the weight of new persons is (b + na) that means: Weight of new persons = Weight of removed person + No. of persons x Increase in average Here, n=4, a=3, b=120 Using these values in shortcut, we get 120 + 4x3 = 120+12 = 132 Hence, Weight of new person = 132 kg

30. The average age of 8 persons in a committee is increased by 2 years when two men aged 35 years and 45 years are substituted by two women. Find the average age of these two women.
  A.  50 years
  B.  43 years
  C.  48 years
  D.  55 years
     
   
View Answer

Shortcut: The average weight of 'n' persons is increased by 'a' kg when some of them who weight 'b' kg are replaced by the same number of persons. Then the weight of new persons is (b + na) that means: Weight of new persons = Weight of removed person + No. of persons x Increase in average Here, n=8, a=2, b = 35+45 = 80 Using these values in shortcut, we get 80 + 8x2 = 80+16 = 96 Hence, the average weight of new person =
96 / 2
= 48 years

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