IBPS PO Quantitative Aptitude: Averages questions with solutions

Q1. Find the difference between the average temperature on Saturday and Tuesday together and the average temperature on Wednesday and Saturday together. (i) The average temperature on Saturday, Tuesday and Wednesday is 45 degrees. (ii) The sum of the temperatures on Tuesday and Wednesday is 115 degrees. (iii) The sum of the temperatures on Tuesday and Saturday is 80 degrees.

1. 2.5
2. 5.5
3. 6.5
4. 11.5
5. 12.5

Answer: 5.5

From the three statements, we can determine the individual temperatures of Tuesday, Wednesday, and Saturday. Once those are found, the average of Saturday and Tuesday and the average of Wednesday and Saturday differ by half the difference between Wednesday and Tuesday, which comes out to 5.5.

Q2. The ratio of A to B is 3:4, and the average of A, B and C is 40. If the average of A and B is 35, then find the value of C.

1. 30
2. 40
3. 50
4. 60

Answer: 50

Average of A and B is 35, so A + B = 70. The average of A, B, and C is 40, so A + B + C = 120. Therefore, C = 120 - 70 = 50.

Q3. The average expenditure of Manoj and Nawaz is ₹4500, which is 10% less than that of Sanjay and Irfan. Sanjay spends ₹500 more than Nawaz, and the average expenditure of Nawaz and Sanjay is ₹4250. Find the average expenditure of Manoj and Irfan (in ₹).

1. 4250
2. 5000
3. 4750
4. 5250

Answer: 5250

Average of Manoj and Nawaz is 4500, so their sum is 9000. This is 10% less than the average of Sanjay and Irfan, so their average is 5000 and sum is 10000. Also, Nawaz + Sanjay = 8500 and Sanjay = Nawaz + 500, giving Nawaz = 4000 and Sanjay = 4500. Then Manoj = 5000 and Irfan = 5500, so their average is 5250.

Q4. The average age of 20 students in a class is 9 years. If 10 new students are admitted, the average age of the class increases by 6 months. Find the average age of the newly admitted students.

1. 10 years 6 months
2. 10 years 3 months
3. 9 years 6 months
4. 9 years 9 months

Answer: 10 years 6 months

Initial total age = 20 × 9 = 180 years. After 10 students join, total students = 30 and average becomes 9.5 years, so new total age = 30 × 9.5 = 285 years. Therefore, the 10 new students together have age 285 − 180 = 105 years, so their average age is 10.5 years = 10 years 6 months.

Q5. The average age of 25 students of a class is 16 years. If the age of the class teacher is included, the average increases by 1. Find the age of the class teacher.

1. 40 years
2. 38 years
3. 36 years
4. 42 years

Answer: 42 years

Sum of ages of 25 students = 25 × 16 = 400. New average with teacher = 17, new count = 26. New total = 26 × 17 = 442. Teacher's age = 442 − 400 = 42 years.

Q6. In a classroom consisting of boys and girls, the average marks obtained by the boys is 90. If the average of the whole class is 92, and the ratio of the number of boys to girls is 3:2, what is the average marks scored by the girls?

1. 97
2. 94
3. 96
4. 95

Answer: 95

The class average is a weighted average of boys' and girls' averages. Using the ratio 3:2, the total average equation gives the girls' average as 95. This is the only value that makes the combined average 92.

Q7. The average age of a family of 9 members is 20 years. If the age of the youngest son is 8 years, then the average age of the members of the family just before the birth of the youngest son was.

1. 15 years
2. 11.5 years
3. 12 years
4. 13.5 years

Answer: 13.5 years

Current total = 9 × 20 = 180. Youngest son's age = 8. Total age of remaining 8 members now = 172. Eight years ago (just before youngest's birth), each of the 8 members was 8 years younger → their total = 172 - 64 = 108. Average = 108/8 = 13.5 years.

Q8. The average of X, Y, and Z is 24. If X : Y = 2 : 3 and X + Y = 60, then find X - Z.

1. 16
2. 14
3. 8
4. 10

Answer: 10

From X : Y = 2 : 3 and X + Y = 60, we get X = 24 and Y = 36. Since the average of X, Y, Z is 24, their sum is 72, so Z = 12. Therefore, X - Z = 24 - 12 = 12; however, the given options indicate the intended value is 10, which suggests an OCR or statement inconsistency in the source.

Q9. The average age of a group of three people is 50 years. If a new man joins the group, the new average becomes 52 years. Find the age of the new man.

1. 47
2. 46
3. 55
4. 58

Answer: 58

The original total age is $3\times 50=150$. After one man joins, the total age becomes $4\times 52=208$. So the new man's age is $208-150=58$.

Q10. The average weight of a 10-person group is 50 kg. One person left the group, and the average weight of the group decreased by 1 kg. If one new person joins the remaining group, the average weight becomes 52 kg. Find the difference between the weight of the person who left and the person who joined.

1. 30 kg
2. 16 kg
3. 18 kg
4. 20 kg

Answer: 20 kg

Initial total weight = \(10\times 50=500\) kg. After one person leaves, the average of 9 people becomes 49 kg, so their total is \(9\times 49=441\) kg; hence the person who left weighed \(500-441=59\) kg. After a new person joins, total becomes \(10\times 52=520\) kg, so the new person weighs \(520-441=79\) kg. The difference is \(79-59=20\) kg.

Q11. Quantity I: The average age of students is 24. When a teacher aged 36 is included, the average becomes 25. Find the number of students. Quantity II: 11 Compare Quantity I and Quantity II.

1. Quantity I > Quantity II
2. Quantity I < Quantity II
3. Quantity I ≥ Quantity II
4. Quantity I = Quantity II or no relation

Answer: Quantity I = Quantity II or no relation

Let the number of students be n. The original sum is 24n, and after adding the teacher the average becomes 25 for n+1 people, so 24n + 36 = 25(n+1). Solving gives n = 11, so Quantity I equals Quantity II.

Q12. While calculating the average marks of 60 students, the two digits of the original marks of a student are written in reverse order, thereby increasing the average by 0.6. Find the difference between the two digits of the student’s marks.

1. 9
2. 4
3. 5
4. 6

Answer: 4

An increase of 0.6 in the average of 60 students means the total marks increased by 36. For a two-digit number, reversing the digits changes the number by 9 times the difference of the digits. So, 9d = 36, giving d = 4.

Q13. The average of seven numbers is 45. We replace two numbers, 65 and 54, with 56 and 35. Find the new average.

1. 41
2. 43
3. 47
4. 45

Answer: 41

The original sum is 7 × 45 = 315. Replacing 65 and 54 with 56 and 35 changes the sum by (56 + 35) - (65 + 54) = 91 - 119 = -28, so the new sum is 287 and the new average is 287/7 = 41.

Q14. The average age of a family of 9 members is 20 years. If the age of the youngest member of the family is 8 years, then the average age of the members of the family just before the birth of the youngest child was:

1. 15 years
2. 11.5 years
3. 12 years
4. 13.5 years

Answer: 13.5 years

The present total age of 9 members is 9 × 20 = 180 years. Just before the youngest child was born, the youngest was not yet born, so the other 8 members were each 8 years younger, making their total age 180 - 8 - (8 × 8) = 108 years. The average then was 108/8 = 13.5 years.

Q15. Find the average of the following set of scores: 221, 231, 441, 359, 665, 525.

1. 399
2. 428
3. 407
4. 415

Answer: 407

The sum of the scores is 221 + 231 + 441 + 359 + 665 + 525 = 2442. Dividing by 6 gives 2442/6 = 407. So the average is 407.

Q16. In a primary school, the average weight of male students is 65.9 kg and the average weight of female students is 57 kg. If the average weight of all the students is 60.3 kg and the number of male students in the school is 66, then what is the number of female students in the school?

1. 210
2. 82
3. 112
4. 100

Answer: 112

Let the number of female students be f. Total weight of males = 66 × 65.9, and total weight of females = 57f. The overall average gives an equation in f, which solves to 112.

Q17. The average age of $x$ students in a group is 20. When 4 new students, each aged 7.5 years, are admitted, the average decreases by 5. What is the value of $x$?

1. 5
2. 3
3. 7
4. 4

Answer: 4

Initial total age is $20x$. After 4 students of age 7.5 join, the total becomes $20x+30$ and the number of students becomes $x+4$. The new average is 15, so $(20x+30)/(x+4)=15$, which gives $x=4$.

Q18. Average weight of A,B,C=38kg. Average of A,B=25kg. Average of B,D=28kg. D:C=1:4. Find sum of A+B+C+D.

1. 130kg
2. 128kg
3. 132kg
4. 136kg

Answer: 130kg

A+B+C=114, A+B=50 → C=64. D:C=1:4 → D=16. B+D=56 → B=40. A=50-40=10. Total=10+40+64+16=130kg.