BANK & INSURANCE (AVERAGE) PART 2

Total Questions: 45

21. Average weight of a boy and a girl in a class is 50 kg and 40 kg, respectively and the average weight of a student (boy + girl) of the class is 44.5 kg. Find the number of boys in the class, if the number of girls in the class is 55.

Correct Answer: (c) 45
Solution:Let the number of boys in the class be ‘x’
According to question:
(50 X x) + (40 X 55) = 44.5 X (x + 55)
50x + 2200 = 44.5x + 2447.5
5.5x = 247.5
x = 45
Therefore, number of boys = 45

22. The average weight of three persons is 43 kg. If the weight of second person is 1.5 times the weight of first person and the weight of third person is 20% more than the weight of second person, then find the difference between the weight of third person and first person.

Correct Answer: (e) 24 kg
Solution:Let the weight of first person be ‘x’ kg
The weight of second person will be = 1.5 X x = ‘1.5x’ kg
The weight of third person will be = 1.5x × (120/100) = ‘1.8x’ kg
Average of all three persons will be = {(1.8x + 1.5x + x)/3} = (4.3x/3) kg
Given,
(4.3x/3) = 43
4.3x = 129
x = 30
The weight of first person = x = 30 kg
The weight of third person = 1.8x = 1.8 X 30 = 54 kg
Required difference = 54 - 30 = 24 kg

23. The average score obtained by 20 students in a class test is 58 marks. The top place was shared by 3 people who got the same score. If the lowest score was 50 marks, then which of the following could be the highest score obtained by toppers? (Marks scored by each student is a whole number)

Correct Answer: (e) 103
Solution:To maximize the toppers score, we must minimize the scores of everyone else.
So, let the scores of other 17 students be 50 marks each.
So, total marks obtained by 17 students = 50 × 17 = 850
Remaining marks = 1160 - 850 = 310
So, score of toppers = 310 ÷ 3 = 103 marks + 1 additional mark
This additional mark could be obtained by any other student.

24. In an exam, ‘A’ obtained 50% more marks than ‘D’ and 20% more marks than ‘C’. The average of the marks obtained by ‘A’ and ‘B’ is 6 more than the average of the marks obtained by ‘B’ and ‘C’. Find the marks scored by ‘D’.

Correct Answer: (b) 48  
Solution:Let the marks scored by ‘D’ = ‘y’
Then, marks scored by ‘A’ = y X 1.5 = ‘1.5y’
Marks scored by ‘C’ = 1.5y ÷ 1.2 = ‘1.25y’
Let the marks scored by ‘B’ = ‘k’
According to the question,
(1.5y + k) ÷ 2 = (1.25y + k) ÷ 2 + 6
Or, 1.25y + k + 12 = 1.5y + k
So, 0.25y = 12
So, y = 48

25. A, B, C and D are four salesmen. In the first month they received a commission of Rs. 3200 from their company and divided it in the ratio of 2 : 3 : 4 : 7. In the second month the commission doubled, the amount was divided in the ratio 3 : 4 : 5 : 4. In the third month the commission tripled when compared to the first month and they shared it in the ratio of 4 : 7 : 3 : 2 and in the fourth month the commission became half of the previous month and they shared it in the ratio of 4 : 3 : 5 : 4. What was the average monthly earning of C over the period?

Correct Answer: (a) Rs. 1,525  
Solution:Total commission in first month = Rs. 3200
Total commission in second month = Rs. 6400
Total commission in third month = Rs. 9600
Total commission in fourth month = Rs. 4800
C’s share in the commission = 4/16 of 3200 + 5/16 of 6400 + 3/16 of 9600 + 5/16 of 4800
= 800 + 2000 + 1800 + 1500 = Rs. 6100
C’s average monthly earnings = 6100/4 = Rs. 1525.

26. The average age of all the team mates of a football team is 62.5. The average age of 4 team mates among them are 60. The average age of the remaining team mates are 63. If the team is divided into three categories namely A, B and C and the number of players in category C is 3/8 of the total team mates, then what is the LCM of the number of players in category A and B, given that number of players in A is twice the number of players in B?

Correct Answer: (b) 10  
Solution:Total number of team mates: x
Total age of all the team mates = 62.5x
Average age of 4 team mates = 60
Total age of 4 team mates = 60 × 4 = 240
Total age of x - 4 team mates = (x - 4) × 63
63(x - 4) + 240 = 62.5x
x = 24
Total team mates: 24.
Number of players in category C = 3/8 × 24 = 9
Let the number of players in B be x
Then the number of players in A = 2x
2x + x = 24 - 9 = 15
x = 5
Number of players in A and B are 10 and 5 respectively.
LCM of 10 and 5 = 10

27. A group of 10 friends go on a trip and the average age of the group of friends is 25 years. Some more friends join their group and the average age of the group decreases by 1. The sum of, the number of new friends who joined the group later and their average age is 27. Find the total age of the group of friends who joined the group later?

Correct Answer: (a) 110 years  
Solution:

Let, the number of friends who joined the group later be ‘n’ and their average age be ‘x’.
According to question,
n + x = 27
x = 27 - n ...(i)

After the new friends joined the group their average decreases by 1. So, the new average of the total group is 24 years.
(10 × 25 + n × x) / (10 + n) = 24
250 + n (27 - n) = 240 + 24n
250 + 27n - n² = 240 + 24n
n² + 24n - 27n - 250 + 240 = 0
n² - 3n - 10 = 0
(n + 2)(n - 5) = 0

So, n = 5
And, x = 27 - 5 = 22
Therefore, total age of the new friends who joined the group later = 22 × 5 = 110 years

28. The average number of goals scored per match by a football player in matches where he was in the team of starting 11 is 1.5 and the average number of goals scored by the player in matches where he came as a substitute is 0.5. The player scored 390 goals more in matches where he was in the team of starting 11 than in matches in which he came on as a substitute. If he played 388 matches in total, find the average number of goals scored by the player per match?

Correct Answer: (e) 1.253
Solution:Let the number of matches in which the player was in the team of starting 11 be x and the matches in which the player came on as a substitute be y.
Thus x + y = 388 ---- (1): Number of goals scored in matches in which the player was in the team of starting 11 = Average × number of matches = 1.5x
Number of goals scored in matches in which he came on as a substitute = 0.5y
Thus, 1.5x = 0.5y + 390 ---- (2)
Solving both equations for x and y, we have x = 292 and y = 96.
So, the total number of goals scored by the player = 1.5 × 292 + 0.5 × 96 = 486 goals.
Therefore, average number of goals scored per match = 486 ÷ 388 = 1.253

29. The average weight of P, Q, R and S is 40 kg. Two new people T and U, whose average weight is 37.5 kg, are also included in the group. Again a new person V replaces P, and then the new average of 6 persons becomes 43 kg. If weight of R is twice the weight of Q and weight of S is half the weight of V then what is the average weight of Q and S?

Correct Answer: (b) 30.5 kg  
Solution:Total weight of P, Q, R and S = 40 × 4 = 160 kg
Total weight of P, Q, R, S, T and U = 160 + 75 = 235kg
Total weight of Q, R, S, T, U and V = 43 × 6 = 258 kg
Total weight of Q, R, S and V = 258 - 75 = 183 kg
According to question,
Q + 2Q + S + 2S = 183
Q + S = 61
Average weight of Q and S = 61/2 = 30.5 kg

30. The average age of 40 children and 5 teachers in a school is 12 years and 35 years, respectively. Five children, out of 40, whose average age is 18 years and two teachers, out of 5, whose average age is 43 years left the school and further 8 new children whose average age is 9.125 years joined the school. What is the present average age of the teachers and students present in the school?

Correct Answer: (c) 12 years
Solution:Total age of 40 students = 40 × 12 = 480 years
Total age of 5 teachers = 5 × 35 = 175 years
Total age of (40 - 5 + 8 = 43) students after 5 students left and 8 students joined
= (480 - 5 × 18 + 8 × 9.125) years
= 480 - 90 + 73
= 463 years
Total age of 3 teachers after two teachers left = 35 × 5 - 43 × 2 = 89 years
Now, total age of 43 students and 3 teachers = 463 + 89 = 552 years
Therefore, required average = 552/46 = 12 years