Average Aptitude Solved Examples: Set 02 - ObjectiveBooks

# Average Aptitude Solved Examples: Set 02

## Average Aptitude Problems with Solutions: Set 02

Question No. 01
A cricketer, whose bowling average is 12.4, takes 5 wickets for 26 runs and thereby decreases his average by 0.4. The number of wickets taken by him before his last match is
(A) 85
(B) 82
(C) 84
(D) 83

Explanation:
Let the number of wickets taken before the last match be x.
Then, (12.4x + 26)/(x + 5) = 12
=> 12.4x + 26 = 12x + 60
=> 0.4x = 34
=> x = 34/0.4 = 340/4 = 85

Question No. 02
The average weight of men ‘A’, ‘B’ and ‘C’ is 84 kg. Another man ‘D’ joints the group and the average now becomes 80 kg. If another man ‘E’, whose weight is 3 kg more than that of ‘D’, replaces ‘A’, then the average weight of ‘B’ ‘C’ ‘D’ and ‘E’ becomes 79 kg. The weight of ‘A’ is
(A) 70 kg
(B) 72 kg
(C) 75 kg
(D) 80 kg

Explanation:
A + b + C = (84 × 3) = 252 kg
A + b + C + D = (80 × 4) = 320 kg.
Therefore, D = (320 - 252) kg = 68 kg.
Given, E = (68 + 3) kg = 71 kg.
Therefore, B + C + D + E = (79 × 4) = 316 kg.
Now, (A + b + C + D) - (B + C + D + E) = (320 - 316) kg = 4 kg.
So, A - E = 4 kg.
=> A = 4 + E = 75 kg.

Question No. 03
The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.
(A) 47.55 kg
(B) 48 kg
(C) 48.55 kg
(D) 49.25 kg

Explanation:
Required average = {(50.25 × 16) + (45.15 × 8)} / (16 + 8)
= (804 + 361.20)/24
= 1165.20/24
= 48.55

Question No. 04
The average age of a class is 15.8 years. The average age of the boys in the class is 16.4 years while that of girls is 15.4 years. What is the ratio of boys to girls in the class?
(A) 1 : 2
(B) 3 : 4
(C) 3 : 5
(D) 2 : 3

Explanation:
Let the ratio be k : 1
Then, (k × 16.4) + (1 × 15.4) = (k + 1) × 15.8
Or, (16.4 - 15.8) k = (15.8 - 15.4)
Or, k = 0.4/0.6 = 2/3
Therefore, the required ratio = 2/3 : 1 = 2 : 3

Question No. 05
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:
(A) 35 years
(B) 40 years
(C) 50 years
(D) None of these

Explanation:
Sum of the present ages of husband, wife and child = {(27 × 3) + (3 × 3)} years = 90 years.
Sum of the present ages of wife and child = {(20 × 2) + (5 × 2)} years = 50 years.
∴ Husband's present age = (90 - 50) years = 40 years.

Question No. 06
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:
(A) 17 kg
(B) 20 kg
(C) 26 kg
(D) 31 kg

Explanation:
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 × 3) = 135 …...... (i)
A + B = (40 × 2) = 80 ......... (ii)
B + C = (43 × 2) = 86 .........(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 ........ (iv)
Subtracting (i) from (iv), we get: B = 31.
∴ B's weight = 31 kg.

Question No. 07
Mr. 'A' travels to Mr. 'B' 150 km away at an average speed of 55 km per hour and returns at 45 km per hour. His average speed for the whole journey in km per hour is
(A) 52.5
(B) 48.5
(C) 49.5
(D) 47.5

Explanation:
Average speed = 2xy/(x + y)
= (2 × 55 × 45)/(55 + 45) km/hr
= 49.5 km/hr.

Question No. 08
The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
(A) 0
(B) 1
(C) 10
(D) 19

Explanation:
Average of 20 numbers = 0.
∴ Sum of 20 numbers (0 × 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).

Question No. 09
A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is:
(A) 10
(B) 20
(C) 40
(D) 73

Explanation:
Let there be x pupils in the class
Total increase in marks = (x × ½) = x/2
x/2= (83 - 63)
=> x/2= 20
=> x = 40

Question No. 10
A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
(A) 28 4/7
(B) 31 5/7
(C) 32 1/7
(D) None of these

Explanation:
Required average = {(67 × 2) + (35 × 2) + (6 × 3)} / (2 + 2 + 3)
= (134 + 70 + 18)/7
= 222/7 = 31 5/7 years.

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