Level 1
Ages MCQs set 2 for ANF Constable (BS-5) Mathematics — 20 solved questions.
Q1. The average height of five pupils is 68 inches. If one pupil is 70 inches and three others are 76 inches each, then what is the height (in inches) of the fifth pupil?
Answer: 42
Explanation: Total height = 5×68 = 340; sum of four known pupils = 70+76+76+76 = 298; fifth pupil = 340−298 = 42 inches.
Q2. The average age of a group of 5 students is 18 years. When a new student joins the group, the average age increases to 19 years. What is the age of the new student?
Answer: 24 years
Explanation: Old total age = 5×18 = 90; new total = 6×19 = 114; new student's age = 114−90 = 24 years.
Q3. The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
Answer: 19
Explanation: If 19 numbers are positive, their sum is cancelled by 1 negative number; at most 19 numbers can be greater than zero.
Q4. A library has an average of 510 visitors on Sunday and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is___________?
Answer: 285
Explanation: 30-day month starting Sunday has 5 Sundays and 25 other days; total visitors = 5×510+25×240 = 8550; average = 8550/30 = 285.
Q5. Ahmad reads 24 pages of a book in 15 minutes. The rate of pages read per minute by him will be:
Answer: 1.6
Explanation: Rate = 24 pages ÷ 15 minutes = 1.6 pages per minute.
Q6. The average age of A, B, C, D, and E is 40 years. The average age of A and B is 35 years and the average of C and D is 42 years. What is the age of E?
Answer: 46 years
Explanation: Total age of five people = 5×40 = 200; subtracting A+B (70) and C+D (84) gives E = 200 − 70 − 84 = 46 years.
Q7. The average of the two-digit numbers, which remain the same when the digits interchange their positions, is__________?
Answer: 55
Explanation: Two-digit numbers unchanged on reversing digits are 11, 22, 33, …, 99 (nine numbers); their average = (11 + 99)/2 = 55.
Q8. The average of first 10 natural numbers is____________?
Answer: 5.5
Explanation: Sum of first 10 natural numbers = n(n+1)/2 = 10×11/2 = 55; average = 55/10 = 5.5.
Q9. The average of first 10 even numbers is___________?
Answer: 11
Explanation: First 10 even numbers are 2, 4, 6, …, 20; their sum = 110 and average = 110/10 = 11.
Q10. The age of a father is twice that of the elder son. Ten years hence the age of the father will be three times of that of the younger son. If the difference of ages of the two sons is 15 years, the age of the father is:
Answer: 50 years
Explanation: Let the younger son's age be y; elder son = y+15, father = 2(y+15). In 10 years the father is 3 times the younger son: 2y+40 = 3y+30, giving y = 10 and father's age = 50.
Q11. Ali is twice as old as his youngest brother. If the difference between their ages is 15 years, how old is his youngest brother?
Answer: 15 years
Explanation: If the youngest brother is x years old and Ali is 2x, then 2x − x = 15, so x = 15 years.
Q12. The average of ten positive numbers is x. If each number is increased by 10%, then x:
Answer: Is increased by 10%
Explanation: When every number increases by 10%, the total increases by 10%, and so does the average x; therefore x is increased by 10%.
Q13. 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 of
Answer: 23 years
Explanation: The correct value is 23 years. Apply the formula or arithmetic step shown in the question and
Q14. The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?
Answer: 9
Explanation: Sum of all 9 = 81; first 5 sum = 50; last 5 sum = 40; the 5th observation = 50 + 40 − 81 = 9.
Q15. In one year, the population, of a village increased by 10% and in the next year, it decreased by 10%. If at the end of 2nd year, the population was 7920, what was it in the beginning?
Answer: 8000
Explanation: After a 10% increase then 10% decrease, the net factor is 0.99; so original population = 7920/0.99 = 8000.
Q16. A building contractor employs 20 male, 15 female and 5 child workers. To a male worker he pays Rs.25 per day, to a female worker Rs.20 per day and a child worker Rs.8 per day. The average wage per day paid by the contractor is__________?
Answer: Rs0.21
Explanation: Total daily wages = 20×25 + 15×20 + 5×8 = 500 + 300 + 40 = Rs. 840; average = 840 ÷ 40 = Rs. 21 per worker.
Q17. The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group?
Answer: 23
Explanation: Let initial members = n; new total weight = 48n + 78 + 93 = 51(n + 2); solving gives 171 − 102 = 3n, so n = 23.
Q18. The average of non-zero number and its square is 5 times the number. The number is__________?
Answer: 9
Explanation: (x + x²)/2 = 5x simplifies to x² − 9x = 0; the non-zero solution is x = 9.
Q19. The average height of 35 boys in a class was calculated as 180cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round
Answer: 178.29 cm
Explanation: The recorded height was 60 cm too high; corrected total = 35 × 180 − 60 = 6,240; actual average = 6,240 ÷ 35 ≈ 178.29 cm.
Q20. A student scored an average of 80 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?
Answer: 80
Explanation: From the three averages: P+C+M=240, P+M=180, P+C=140; solving gives P = 80.