Join PAF: Airman Initial Test Mathematics Ages — Set 3

1. Question 1

   Q1. Find out the average of A and B if the given value of 16A + 16B = 48.

   • A) 1.5
   • B) 2
   • C) 5.3
   • D) 7.4

   Answer: 1.5

   Explanation: 16A + 16B = 48 → 16(A+B) = 48 → A+B = 3. Average = (A+B)/2 = 1.5.

2. Question 2

   Q2. If x² - y² = 28 and x - y = 8, what is the average of x and y?

   • A) 3.5
   • B) 1.75
   • C) 7
   • D) 8

   Answer: 1.75

   Explanation: (x−y)(x+y) = 28 and x−y = 8, so x+y = 3.5; the average = (x+y)/2 = 1.75.

3. Question 3

   Q3. The average weight of 10 people increased by 1.5 kg when one person of 45 kg is replaced by a new man. Then the weight of the new man is:

   • A) 50 kg
   • B) 60 kg
   • C) 70 kg
   • D) 75 kg

   Answer: 60 kg

   Explanation: Total weight increase = 10 × 1.5 = 15 kg. New man's weight = 45 + 15 = 60 kg.

4. Question 4

   Q4. What is the average of the first five multiples of 9?

   • A) 20
   • B) 27
   • C) 28
   • D) None of these

   Answer: 27

   Explanation: The correct value is 27. Apply the formula or arithmetic step shown in the question and

5. Question 5

   Q5. Average weight of 30 students of a class is 40 kg. If the weight of a teacher be included, the average increases by 1 kg. What is the weight of the teacher?

   • A) 71kg
   • B) 81kg
   • C) 61kg
   • D) 51kg

   Answer: 71kg

   Explanation: New total = 31 students with average 41 kg; teacher's weight = 31 × 41 − 30 × 40 = 1271 − 1200 = 71 kg.

6. Question 6

   Q6. A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, there by increasing his average by 6 runs. His new average is_____________?

   • A) 48 runs
   • B) 52 runs
   • C) 55 runs
   • D) 60 runs

   Answer: 48 runs

   Explanation: Let old average = A; then 10A + 108 = 11(A+6) gives A = 42, and new average = 42 + 6 = 48 runs.

7. Question 7

   Q7. The average of first ten prime numbers which are odd is____________?

   • A) 12.9
   • B) 13.8
   • C) 15.8
   • D) 17

   Answer: 15.8

   Explanation: The first 10 odd primes are 3,5,7,11,13,17,19,23,29,31; their sum = 158 and average = 15.8.

8. Question 8

   Q8. At 3:00 AM, the temperature was 13°C below zero. By noon, it had risen to 32°C. What was the average hourly increase in temperature?

   • A) 5°C
   • B) 7.5°C
   • C) 45°C
   • D) (19/6)°C

   Answer: 5°C

   Explanation: Temperature rose from −13°C to +32°C (a rise of 45°C) over 9 hours (3 AM to noon). Average hourly increase = 45/9 = 5°C.

9. Question 9

   Q9. The average of the marks of 12 students in a class is 36. If the marks of each student are doubled, find the new average?

   • A) 72
   • B) 45
   • C) 37
   • D) 79

   Answer: 72

   Explanation: Doubling each mark doubles the total sum, so the average also doubles: 36 × 2 = 72.

10. Question 10

    Q10. The average height of 50 pupils in a class is 150 cm. Five of them whose height is 146 cm, leave the class and five others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is __________.

    • A) 149
    • B) 151
    • C) 152
    • D) 153

    Answer: 151

    Explanation: Removing 5 pupils at 146 cm and adding 5 at average 156 cm increases the total by 50 cm; new average = (7500+50)/50 = 151 cm.

11. Question 11

    Q11. The average of first 10 odd numbers is________?

    • A) 11
    • B) 10
    • C) 12
    • D) 17

    Answer: 10

    Explanation: The first 10 odd numbers are 1,3,5,...,19; their sum = 10² = 100, giving an average of 10.

12. Question 12

    Q12. The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 7th number?

    • A) 46
    • B) 32
    • C) 68
    • D) 51

    Answer: 46

    Explanation: Sum of 13 numbers = 780; sum of first 7 = 399; sum of last 7 = 427; 7th number = 399 + 427 − 780 = 46.

13. Question 13

    Q13. The average of 5 numbers is 42. If a sixth number, 48, is included, what is the new average?

    • A) 44
    • B) 45
    • C) 43
    • D) 46

    Answer: 43

    Explanation: New total = 5×42 + 48 = 258; new average = 258/6 = 43.

14. Question 14

    Q14. The average marks of a class of 30 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?

    • A) 50
    • B) 47.5
    • C) 59
    • D) 52.5

    Answer: 52.5

    Explanation: Weighted average = (30 × 40 + 50 × 60) ÷ (30 + 50) = 4,200 ÷ 80 = 52.5.

15. Question 15

    Q15. The average monthly income of P and Q is Rs. 5,050. The average monthly income of Q and R is Rs. 6,250. The average monthly income of P and R is Rs. 5,200. What will P's monthly income be?

    • A) Rs. 3500
    • B) Rs. 4000
    • C) Rs. 4050
    • D) Rs. 5000

    Answer: Rs. 4000

    Explanation: P+Q = 10100, Q+R = 12500, P+R = 10400; total 2(P+Q+R) = 33000, so P = 16500 − 12500 = Rs. 4000.

16. Question 16

    Q16. The average of 50 numbers is 30. If two numbers, 35 and 40, are discarded, what is the average of the remaining numbers?

    • A) 30
    • B) 32
    • C) 34
    • D) None of these

    Answer: None of these

    Explanation: The correct value is None of these. Apply the formula or arithmetic step shown in the question and

17. Question 17

    Q17. A is two years older than B, and B is twice as old as C. If the sum of the ages of A, B, and

    • A) 9 years
    • B) 10 years
    • C) is 27, how old is B? Ages 11 years
    • D) 12 years

    Answer: 10 years

    Explanation: Let C = c; then B = 2c and A = 2c + 2; summing to 27 gives 5c + 2 = 27, so c = 5 and B = 10 years.

18. Question 18

    Q18. The present age of a father is 3 times that of his son. Five years ago, the father's age was 4 times the age of his son. What is the present age of the son?

    • A) 10 years
    • B) 15 years
    • C) 12 years
    • D) 20 years

    Answer: 15 years

    Explanation: Let son's current age = x; father = 3x; five years ago 3x − 5 = 4(x − 5), giving x = 15 years.

19. Question 19

    Q19. If the average (arithmetic mean) of 8, 12, 15, 21, x, and 11 is 17, then what is x?

    • A) 3
    • B) 15
    • C) 17
    • D) 35

    Answer: 35

    Explanation: Sum of all six values = 17×6 = 102; subtracting the known values (8+12+15+21+11 = 67) gives x = 35.

20. Question 20

    Q20. The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary?

    • A) Rs. 2000
    • B) Rs. 2400
    • C) Rs. 3600
    • D) Rs. 4800

    Answer: Rs. 3600

    Explanation: Original total salary = 20×1500 = 30000; with manager, total = 21×1600 = 33600; manager's salary = 33600 − 30000 = Rs. 3600.