Average Aptitude Solved Examples: Set 01

Average Aptitude Problems with Solutions: Set 01

Question No. 01
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) 30 years
(B) 35 years
(C) 45 years
(D) 52 years

Explanation:
Total age of 30 boys = 14 × 30 = 420 years
Total age when the teacher is included = 15 × 31 = 465 years
∴ Age of the class teacher = 465 - 420 = 45 years

Alternate Method: Direct Formula
Age of new entrant = New average + (No. of old members × change in average)
= 15 + 30 (15 - 14) = 45 years.

Question No. 02
The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
(A) 23 years
(B) 24 years
(C) 25 years
(D) None of these

Explanation:
Let the average age of the whole team by x years.
∴ 11x - (26 + 29) = 9(x -1)
=> 11x - 9x = 46
=> 2x = 46
=> x = 23.
So, average age of the team is 23 years.

Question No. 03
The average age of boys in the class is twice the number of girls in the class. If the ratio of boys and girls in the class of 36 be 5 : 1, what is the total of the ages (in years) of the boys in the class?
(A) 380
(B) 342
(C) 372
(D) 360

Explanation:
Number of boys = (36 × 5/6) = 30 years
Numbers of girls = 6
Average age of boys = (2 × 6) = 12 years
Total age of boys = (30 × 12) years = 360 years.

Question No. 04
A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?
(A) Rs. 7.98
(B) Rs. 8
(C) Rs. 8.50
(D) Rs. 9

Explanation:
Total quantity of petrol consumed in 3 years
= {(4000/7.50) + (4000/8) + (4000/8.50)} litres
= 4000 {(2/15) + (1/8) + (2/17)} litres
= (76,700/51) litres
Total amount spent = Rs. (3 × 4000) = Rs. 12,000
∴ Average cost = Rs. (12,000 × 51)/ 76,700
= Rs. 6120/767
= Rs. 7.98

Question No. 05
In Ankit's opinion, his weight is greater than 65 kg but less than 72 kg. His sister does not agree with Ankit and she thinks that Ankit's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Ankit?
(A) 67 kg.
(B) 68 kg.
(C) 69 kg.
(D) None of these

Explanation:
Let Ankit's weight be x kg.
According to Ankit, 65 < x < 72
According to Ankit's sister, 60 < x < 70
According to Ankit's mother, x ≤ 68
The values satisfying all the above conditions are 66, 67 and 68.
∴ Required average = (66 + 67 + 68)/3 = 201/3 = 67 kg.

Question No. 06
Indian shooting team of 8 persons joins in a shooting competition. One of them scored 85 points. If he had scored 92 points, the average score for the team would have been 84. The numbers of points, the team scored was
(A) 672
(B) 665
(C) 645
(D) 588

Explanation:
Let the total score be x.
Therefore, (x + 92 - 85)/8 = 84
=> (x + 7) = 672
=> x = 665

Question No. 07
If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is:
(A) 53.33
(B) 54.68
(C) 55
(D) None of these

Explanation:
Required average = {(55 × 50) + (60 × 55) + (45 × 60)} / (55 + 60 + 45)
= (2750 + 3300 + 2700)/160
= 8750/160
= 54.68

Question No. 08
Three years ago, the average age of Raju, Ranjan and Ravi was 27 years and that of Ranjan and Ravi, 5 years ago was 20 years. Raju’s present age is
(A) 30 years
(B) 35 years
(C) 40 years
(D) 48 years

Explanation:
Present age of (Raju + Ranjan + Ravi) = {(27 × 3) + (3 × 3)} = 90 years.
Present age of (Ranjan + Ravi) = {(20 × 2) + (2 × 5)} = 50 years.
Therefore, Raju’s present age = (90 - 50) = 40 years.

Question No. 09
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:
(A) 3500
(B) 4000
(C) 4050
(D) 5000

Explanation:
Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 × 2) = 10,100 …..... (i)
Q + R = (6250 × 2) = 12,500 …….. (ii)
P + R = (5200 × 2) = 10,400 …….. (iii)
Adding (i), (ii) and (iii), we get:  2(P + Q + R) = 33,000    or   P + Q + R = 16,500 …..... (iv)
Subtracting (ii) from (iv), we get P = 4000.
∴ P's monthly income = Rs. 4000

Question No. 10
The average of 5 consecutive numbers is ‘n’. If the next two numbers are also included, the average will
(A) Increase by 1
(B) Remain same
(C) Increase by 1.4
(D) Increase by 2

Explanation:
Let, 5 consecutive numbers be, x, x+1, x+2, x+3 and x+4
Their average is = (5x + 10)/5 = (x + 2)
The next two numbers are = (x + 5) and (x + 6)
Therefore, Average of the numbers = [(5x + 10) + (x + 5) + (x + 6)]/7 = (7x + 21)/7 = (x +3)
So, the average increased by 1.