Arithmatical - Average

DIRECTIONS : Problems based on Average.
20. A students was asked to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of x?
  A.  3
  B.  7
  C.  17
  D.  31
Solution
Clearly, we have (3+11+7+9+15+13+8+19+17+21+14+x/12) =12
Number in place of x is
137+x=144
x= 144-137
x= 7.
21. Find the average of all the numbers between 6 and 34 which are divisible by 5.
  A.  18
  B.  20
  C.  24
  D.  30
Solution
Average= (10+15+20+25+30/5)
= 100 / 5
= 20.

22. The average age of a group of persons going for picnic is years. Twenty new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is
  A.  5
  B.  10
  C.  20
  D.  40
Solution
Let the initial number of persons be x. Then
16x + 20 x 15 = 15.5(x+20)
= 0.5x = 10
x = 20.
23. The average weight of 8 persons 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?
  A.  76 kg
  B.  80 kg
  C.  85 kg
  D.  90 kg
Solution
Total weight increased= (8 x 2.5)kg
= 20 kg.
Weight of new person= (65 + 20)kg
= 85 kg.
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