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81. If average of 7 consecutive numbers is 21, what is the difference between the smallest and the largest numbers?
  A.  14
  B.  12
  C.  10
  D.  11
     
   
View Answer

Shortcut:
If average of'n' consecutive odd numbers is 'a', then the difference between the smallest and the largest numbers is given by 2(n-1).
Here, n = 7
Using the value in shortcut, we get: Difference between smallest and the largest numbers = 2(7-1) = 2 x 6 = 12

82. An aeroplane covers the four sides of square field at speeds of 200, 400, 600 and 800 km/hr. Then the average speed of the plane in the entire journey is:
  A.  390 km/hr
  B.  378 km/hr
  C.  384 km/hr
  D.  390 km/hr
     
   
View Answer

Suppose one side of the square be a km. Then, the total distance = 4a km. Total time =
a / 200
+
a / 400
+
a / 600
+
a / 800
=
a / 96
hours
∴ Average speed =
4a x 96 / a
= 384 km/hr

83. The average age of the three girls is 15 years. Their ages are in the ratio 3 : 5 : 7. The the age of the oldest is:
  A.  15 years
  B.  23 years
  C.  19 years
  D.  21 years
     
   
View Answer

Suppose their ages be 3y, 5y and 7y
Average of their ages =
3y+5y+7y / 3
=15 (given)
∴ Total of their ages = 3y + 5y + 7y = 3 x 15
15y = 45
y =
45 / 15

⇒ y = 3
Hence, the age of the oldest = 7 x y = 7 x 3 = 21 years

84. The population of a town increased by 20% during the first year, by 25% during the next year and by 44% during the third year. Find the average rate of increase during 3 years?
  A.  39.75%
  B.  36.25%
  C.  38.67%
  D.  40.67%
     
   
View Answer

Let the population at starting is 100
Population after 1st year = 100 x 1.20 = 120
Population after 2nd year = 120 x 1.25 = 150
Population after 3rd year = 150 x 1.44 = 216
Net increase = 216 - 100 = 116
% increase during 3 years =
116 / 100
x 100 = 116%
% increase per year =
116 / 3
% = 38.67%

85. Out of three given numbers, the first one is twice the second and three times the third. If the average of these numbers is 88, then the difference between first and third is:
  A.  92
  B.  96
  C.  98
  D.  95
     
   
View Answer

Let First no. = a, Second no. =
a / 2
and Third no. =
a / 3

∴ a +
a / 2
+
a / 3
= 3 x 88
11a / 6
= 264
a =
264 x 6 / 11
= 144
Hence, 1st − 3rd = (144 -
1 / 3
x 144) = 96

86. The average age of a family of 6 members is 22 years. If the age of the youngest member be 7 years, the average age of the family at the birth of the youngest member was:
  A.  21 years
  B.  15 years
  C.  18 years
  D.  20 years
     
   
View Answer

Total present age of the family = (6 x 22) = 132 years 7 years ago, their total age = [132 − (7 x 6)] = 90 years At that time, the number of members = 5 ∴ Average age at that time =
90 / 5
years = 18 years

87. The average age of a husband and wife was 23 years when they were married 5 years ago. The average age of the husband, the wife and a child who was born during the interval, is 20 years now. How old is the child now?
  A.  3 years
  B.  5 years
  C.  2 years
  D.  4 years
     
   
View Answer

Present total age of Husband and Wife = [(2 x 23) + (2 x 5)] = 56 years
Present total age of husband, wife and child = 3 x 20 = 60 years
Present age of child = ( 60 − 56) = 4 years

88. Out of the three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 56, the three numbers in order are:
  A.  48,24,92
  B.  48,24,96
  C.  48,22,96
  D.  48,24,98
     
   
View Answer

Let the three numbers are 2y, y and 4y
Average =
2y + y + 4y / 3

=
7y / 3
= 56
∴ y =
3 x 56 / 7
= 24
Hence, three numbers in order are 48, 24 and 96

89. The average age of A, B, C and D, 5 years ago was 45 years. By including X, the present average of all the five is 49 years. The present age of X is:
  A.  45 years
  B.  43 years
  C.  48 years
  D.  42 years
     
   
View Answer

Five years ago, total age of A, B, C and D = (45 x 4) years = 180 years
Total present age of A, B, C, D and X = (49 x 5) years = 245 years
∴ Present age of A, B, C and D = [180 + (5 x 4)] years = 200 years
Hence, the present age of of X = 45 years.

90. The average age of A and B is 20 years. If C were to replace A, the average would be 19 and if C were to replace B, the average would be 21. What are the ages of A, B and C?
  A.  22,18,40
  B.  22,16,20
  C.  22,18,20
  D.  22,18,30
     
   
View Answer

A + B / 2
= 20
⇒ A + B = 20 x 2 = 40 ---------------- (eq 1)
B + C / 2
= 19
⇒ B + C = 19 x 2 = 38 ---------------- (eq 2)
C + A / 2
= 21
⇒ C + A = 21 x 2 = 42 ---------------- (eq 3)
Adding eq 1, eq 2 and eq 3, we get:
(A + B) + (B + C) + (C + A) = 40 + 38 + 42
2(A + B + C) = 120
A + B + C =
120 / 2
= 60
Hence, A + B + C = 60 ------------------- (eq 4)
Now, Subtract (eq 2) from (eq 4)
(A + B + C) − (B + C) = 60 - 38
A = 22
Putting value of A in eq 1, we get:
A + B = 40
22 + B = 40
B = 40 − 22 = 18
Putting value of B in eq 2, we get:
B + C = 38
18 + C = 38
C = 38 − 18 = 20
Hence, Ages of A, B and C are 22 years, 18 years and 20 years respectively.

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