BANK & INSURANCE (AVERAGE) PART 2

Total Questions: 45

11. In a cricket match, 7 players had an average of their runs. Average increases by 10 runs, if the 8th player makes a score of 120 runs. What is the average of the first 7 players?

Correct Answer: (d) 40  
Solution:

Let, the average runs of 7 players be x.
Than total run of seven players
⇒ Average run of player × number of players
⇒ x × 7 = 7x
Total runs of all eight players
⇒ (Total run of seven players + 8th player makes score)
⇒ 7x + 120
The average runs of 8 players
⇒ (Total runs of all eight players/ number of players)
⇒ (7x + 120)/8 ----(i)

But when 8th player score 120 runs than average increase by 10 runs
So, average of eight players = (average runs of 7 players + increment in average):
⇒ x + 10 ----(ii)

From (i) and (ii), we get
⇒ (x + 10) = (7x + 120)/8
⇒ 8x + 80 = 7x + 120
⇒ 8x - 7x = 120 - 80
⇒ x = 40
∴ We assumed that the average runs of 7 players would be x.
∴ The average of the first 7 players is 40 runs.

12. The average weight of 20 men is increased by 2 kg, when one of the men, Which weight 80 kg is replaced by a new man. Find the weight of the new man.

Correct Answer: (c) 120 Kg
Solution:

Total increased weight = 20 × 2 = 40 Kg
The weight of new men = 80 Kg + 40 Kg = 120 Kg

13. Average age of a group of 28 persons is 24 years. If a new person is included then the average age rises by 1 year, then the present age of new person will be which of the following?

Correct Answer: (e) 53
Solution:

Total age of the group = 28 × 24 = 672
When a new person is included the average age rises to 25
⇒ Now, after the inclusion of a new person the average age = 29 × 25 = 725
The difference between total ages before and after the inclusion of the new person is his age
⇒ Present age of the person included
= 725 - 672 = 53

14. The average age of Komal and Sarita is 32 years, the average age of Anita and Sarita is 28 years and the average age of Anita and Komal is 29 years. Find the age of Komal, Sarita and Anita.

Correct Answer: (a) 33 years, 31 years and 25 years
Solution:

According to question:
⇒ (K + S)/2 = 32
⇒ K + S = 64 ----(1)

⇒ (A + S)/2 = 28
⇒ A + S = 56
⇒ S = 56 - A ----(2)

⇒ (A + K)/2 = 29
⇒ A + K = 58
⇒ K = 58 - A ----(3)

Put (2) and (3) in eq. (1)
⇒ 58 - A + 56 - A = 64
⇒ 114 - 2A = 64
⇒ A = 25
⇒ S = 56 - 25
⇒ S = 31
⇒ K = 58 - 25
⇒ K = 33

∴ The present age of Anita, Komal and Sarita is 25, 33 and 31 years.

15. If in the 4th subject, Kamal obtained 18 marks and his average marks increased by 1. Find the average marks scored in first three subjects.

Correct Answer: (d) 14  
Solution:

(Sum of 3 subjects + 18)/4 = (sum of three subjects)/3 + 1

(Sum of 3 subjects + 18)/4 = [(sum of three subjects) + 3]/3

3(Sum of 3 subjects + 18) = 4 [(sum of three subjects) + 3]

Let sum of three subjects is x

⇒ 3x + 54 = 4x + 12
⇒ 54 - 12 = 4x - 3x
⇒ 42 = x

∴ average of 3 subjects is 14 (i.e. 42/3)

16. The average expenditure of a family from January to April is Rs. 15,000 and from May to December is Rs. 30,000. If family saves Rs. 20,000 in that year. Find his monthly average income.

Correct Answer: (c) Rs. 26,666
Solution:Expenditure from January to April = Rs. 60,000
Expenditure from May to December = Rs. 2,40,000
⇒ Total income of a year = Rs. 60,000 + Rs. 2,40,000 + Rs. 20,000
= Rs. 3,20,000
∴ Monthly average income = 3,20,000/12 = Rs. 26,666

17. There are four consecutive odd numbers and four consecutive even numbers. The sum of the four consecutive odd numbers is 120. If the difference of the highest odd number and the smallest even number is 11. Find the sum of the four consecutive even numbers.

Correct Answer: (b) 100  
Solution:Let the four consecutive odd numbers are, x, x+2, x+4 and x+6
x+x+2+x+4+x+6=120
4x+12=120
x = 27
So the odd numbers are-27,29,31,33
Then smallest even number will be = 33-11 = 22
Then the even numbers = 22, 24, 26 and 28 Sum
= 22+24+26+28 = 100

18. In Shatabdi Express, there are 10 boggies which carries on an average of 24 passengers per boggie. If atleast 14 passengers were sitting in each boggie and no boggie has equal number of passengers then maximum, how many passengers can be accomodated in a boggie?

Correct Answer: (a) 78  
Solution:

Total no. of passengers = 24 × 10 = 240
So, in the 9 boggies, total no. of total passengers = 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 = 162
Hence, in 1 boggie. max. passengers = 240 – 162 = 78

19. A lab assistant observes 24 tests and found that the average of their result is 36, but later he realised that he calculated three values as 36, 46 and 28 instead of 43, 52 and 27. Find the difference between the original average and calculated average.

Correct Answer: (d) 0.5  
Solution:Sum of the results of 24 tests = 36 × 24 = 864
Actual sum = 864 - (36 + 46 + 28) + (43 + 52 + 27)
= 876
Actual average = 876/24 = 36.5
Required difference = 36.5 - 36 = 0.5

20. The average weight of a group of certain number of goats is 50 kg. If 5 goats with average weight of 68 kg are removed and 2 goats with average weight of 70 kg are added in the group, then the average weight of the new group of goats becomes 48 kg. Find the original number of goats in the group.

Correct Answer: (c) 28
Solution:Let the original number of goats in the group be ‘y’
Then, total weight of all the goats = 50y kg
According to the question,
50y - 5 × 68 + 2 × 70 = (y - 5 + 2) × 48
Or, 50y - 340 + 140 = (y - 3) × 48
Or, 50y - 200 = 48y - 144
Or, 2y = 56
So, y = (56/2) = 28
Required number of goats = 28