Basic Averages
â–¶ What is the average of 4, 8, and 12?
Answer: 8
Explanation: (4+8+12)/3 = 8.
â–¶ Find the average of 10, 20, 30, 40, and 50.
Answer: 30
Explanation: (10+20+30+40+50)/5 = 30.
â–¶ The average of 5, 7, and 9 is?
Answer: 7
Explanation: (5+7+9)/3 = 7.
â–¶ What is the average of 2, 4, 6, 8, 10?
Answer: 6
Explanation: (2+4+6+8+10)/5 = 6.
â–¶ Find the average of 15 and 25.
Answer: 20
Explanation: (15+25)/2 = 20.
â–¶ The average of 3, 6, 9, 12 is?
Answer: 7.5
Explanation: (3+6+9+12)/4 = 7.5.
â–¶ What is the average of 100 and 200?
Answer: 150
Explanation: (100+200)/2 = 150.
â–¶ Find the average of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Answer: 5.5
Explanation: (1+2+...+10)/10 = 5.5.
â–¶ The average of 20, 30, 40 is?
Answer: 30
Explanation: (20+30+40)/3 = 30.
â–¶ What is the average of 0, 5, 10, 15, 20?
Answer: 10
Explanation: (0+5+10+15+20)/5 = 10.
â–¶ The average of 15 numbers is 40. If each number is increased by 5, what is the new average?
Answer: 45
Explanation: 40+5 = 45.
â–¶ The average of 8 numbers is 25. If one number is excluded, the average becomes 22. What is the excluded number?
Answer: 46
Explanation: (8×25)-(7×22) = 46.
â–¶ The average age of 20 students is 15 years. When the teacher's age is included, the average becomes 16 years. What is the teacher's age?
Answer: 36 years
Explanation: (21×16)-(20×15) = 36.
â–¶ The average weight of 8 students is 60 kg. If one student leaves and the average drops to 59.5 kg, what was the weight of the student who left?
Answer: 64 kg
Explanation: (8×60)-(7×59.5) = 64.
â–¶ The average of 5 numbers is 27. If a sixth number is added and the new average becomes 30, what is the sixth number?
Answer: 45
Explanation: (6×30)-(5×27) = 45.
â–¶ The average marks of 30 students is 50. The average marks of boys is 55 and that of girls is 45. How many boys are there?
Answer: 15
Explanation: 55x+45(30-x)=30×50 ⇒ x=15.
â–¶ The average of 4 consecutive even numbers is 27. What are the numbers?
Answer: 24, 26, 28, 30
Explanation: x+3=27 ⇒ x=24.
â–¶ The average of 6 numbers is 15. If one number is doubled, the new average becomes 17. What is the doubled number?
Answer: 42
Explanation: (6×17)-(6×15)=12, so doubled number is 12 more than original. x=12.
â–¶ The average of 10 numbers is 40. If the average of the first 4 is 35 and the last 4 is 45, what is the average of the middle two numbers?
Answer: 40
Explanation: (10×40)-(4×35)-(4×45)=80, 80/2=40.
▶ The average salary of 20 employees is ₹30,000. If the manager's salary is added, the average becomes ₹31,000. What is the manager's salary?
Answer: ₹51,000
Explanation: (21×31,000)-(20×30,000)=₹51,000.
â–¶ The average of 5 numbers is 18. If one number is excluded, the average becomes 16. What is the excluded number?
Answer: 28
Explanation: (5×18)-(4×16)=28.
â–¶ The average of three numbers is 20. The first is twice the second and the third is 10 more than the second. What are the numbers?
Answer: 30, 15, 25
Explanation: Let x=second; 2x, x, x+10; (2x+x+x+10)/3=20 ⇒ x=15.
â–¶ The average of 7 consecutive odd numbers is 41. What is the largest of these numbers?
Answer: 47
Explanation: Middle=41, largest=41+6/2=44; but 7 odds: 37,39,41,43,45,47,49. Largest=47.
â–¶ The average weight of 12 boxes is 18 kg. If a 10 kg box is replaced with a 26 kg box, what is the new average?
Answer: 19.33 kg
Explanation: (12×18)-10+26=232; 232/12≈19.33.
â–¶ A class has 20 boys averaging 70 marks and 30 girls averaging 85 marks. What is the overall class average?
Answer: 79
Explanation: (20×70+30×85)/50=79.
â–¶ A car travels from A to B at 60 km/h and returns at 40 km/h. What is the average speed for the round trip?
Answer: 48 km/h
Explanation: 2×60×40/(60+40)=48.
â–¶ Find the average of the first 25 natural numbers.
Answer: 13
Explanation: (25×26/2)/25=13.
â–¶ The average of 12 observations is 35. Later, an observation 24 is corrected to 42. Find the new average.
Answer: 36.5
Explanation: (12×35-24+42)/12=36.5.
â–¶The average age of a family of 6 is 30 years. The youngest is 10 years old. What is the average age of the remaining members?
Answer: 34 years
Explanation: (6×30-10)/5=34.
â–¶ A batsman averages 45 in 20 innings. How many runs must he score in his next innings to raise his average to 50?
Answer: 150
Explanation: (21×50)-(20×45)=150.
â–¶ Group A has 10 people averaging 50 kg. Group B has 15 people averaging 60 kg. What is the combined average?
Answer: 56 kg
Explanation: Total weight A = 10 × 50 = 500 kg. Total weight B = 15 × 60 = 900 kg. Total weight = 1400 kg. Total people = 25. Average = 1400 / 25 = 56 kg.
▶ The average price of 5 books is ₹200. When 3 new books are added, the average becomes ₹220. Find the average price of the new books.
Answer: ₹253.33
Explanation: Sum of 5 books = 5 × 200 = ₹1000. Sum of 8 books = 8 × 220 = ₹1760. Sum of new books = 1760 - 1000 = ₹760. Average of new books = 760 / 3 ≈ ₹253.33.
▶ The average temperature for Monday to Wednesday is 30°C. For Tuesday to Thursday, it is 32°C. If Monday is 28°C, what is Thursday's temperature?
Answer: 34°C
Explanation: Sum (Mon-Wed) = 3 × 30 = 90. Mon = 28 → Tue + Wed = 62. Sum (Tue-Thu) = 3 × 32 = 96. Thu = 96 - 62 = 34°C.
â–¶ A man travels 60 km at 30 km/h, 100 km at 50 km/h, and 120 km at 60 km/h. What is the average speed?
Answer: 46.67 km/h
Explanation: Total distance = 280 km. Time = 2 + 2 + 2 = 6 hours. Average speed = 280 / 6 ≈ 46.67 km/h.
â–¶ The average of two numbers is 30. If they are in the ratio 3:5, find the numbers.
Answer: 22.5, 37.5
Explanation: Sum = 2 × 30 = 60. Parts = 3 + 5 = 8. First number = 3/8 × 60 = 22.5. Second number = 5/8 × 60 = 37.5.
â–¶ The average weight of 20 students is 50 kg. If 5 new students of average weight 60 kg join, what is the new average?
Answer: 52 kg
Explanation: Sum of 20 students = 1000 kg. Sum of 5 new = 300 kg. Total sum = 1300 kg. Total students = 25. Average = 1300 / 25 = 52 kg.
â–¶ Find the average of squares of the first 10 natural numbers.
Answer: 38.5
Explanation: Sum of squares = 10 × 11 × 21 / 6 = 385. Average = 385 / 10 = 38.5.
▶ A man spends ₹1500 per month for 6 months and ₹2000 for the next 6 months. What is his average monthly expenditure?
Answer: ₹1750
Explanation: Total expenditure = 9000 + 12000 = ₹21,000. Total months = 12. Average = 21,000 / 12 = ₹1750.
â–¶ The average of 6 non-zero numbers is 15. If one number is zero, what is the average of the remaining five?
Answer: 18
Explanation: Original sum = 6 × 15 = 90. New sum = 90 - 0 = 90. Average of five = 90 / 5 = 18.
â–¶ The average height of 30 boys is 160 cm. If 10 more boys of average height 170 cm join, what is the new average?
Answer: 162.5 cm
Explanation: Sum of 30 boys = 4800 cm. Sum of 10 boys = 1700 cm. Total sum = 6500 cm. Total boys = 40. Average = 6500 / 40 = 162.5 cm.
â–¶ The average age of 10 employees is 35 years. If an employee aged 40 retires and is replaced by a new employee aged 25, what is the new average?
Answer: 33.5 years
Explanation: Original sum = 10 × 35 = 350. New sum = 350 - 40 + 25 = 335. New average = 335 / 10 = 33.5 years.
â–¶ Find the average of all multiples of 7 between 20 and 60.
Answer: 38.5
Explanation: Multiples: 21, 28, 35, 42, 49, 56. Sum = 231. Count = 6. Average = 231 / 6 = 38.5.
â–¶ The average rainfall for 7 days is 5 mm. If the rainfall on the eighth day is 15 mm, what is the new average?
Answer: 6.25 mm
Explanation: Sum for 7 days = 35 mm. Total sum = 50 mm. Average = 50 / 8 = 6.25 mm.
▶ The average cost of 5 items is ₹80. If two items costing ₹70 and ₹90 are removed, what is the average cost of the remaining items?
Answer: ₹80
Explanation: Sum of 5 items = ₹400. Sum after removal = 400 - 70 - 90 = ₹240. Remaining items = 3. Average = 240 / 3 = ₹80.
â–¶ A student's average score increases by 3 after scoring 90 in a test. If his original average was 75 over 10 tests, what was his total score before the 90?
Answer: 768
Explanation: Original sum = 10 × 75 = 750. New sum = 11 × 78 = 858. Score in new test = 90. Total before new test = 858 - 90 = 768.
â–¶ Group A has 8 people averaging 65 kg. Group B has 12 people. The combined average is 70 kg. What is Group B's average?
Answer: 73.33 kg
Explanation: Total weight = 20 × 70 = 1400 kg. Weight of A = 8 × 65 = 520 kg. Weight of B = 1400 - 520 = 880 kg. Average of B = 880 / 12 ≈ 73.33 kg.
â–¶ Find the average of the first 15 even numbers.
Answer: 16
Explanation: First 15 even numbers: 2, 4, ..., 30. Sum = 15/2 × (2 + 30) = 240. Average = 240 / 15 = 16.
â–¶ Find the average of cubes of the first 4 natural numbers.
Answer: 25
Explanation: Cubes: 1, 8, 27, 64. Sum = 100. Average = 100 / 4 = 25.
â–¶ The average age of A and B is 25 years. The average age of B and C is 30 years. The average age of A and C is 27 years. What is A's age?
Answer: 22 years
Explanation: A + B = 50. B + C = 60. A + C = 54. Add all: 2(A + B + C) = 164 → A + B + C = 82. A = 82 - 60 = 22 years.
â–¶ A train covers 300 km at 60 km/h and stops for 1 hour. It then covers 200 km at 50 km/h. What is its average speed?
Answer: 50 km/h
Explanation: Total distance = 500 km. Time for first part = 5 hours. Stop = 1 hour. Time for second part = 4 hours. Total time = 10 hours. Average speed = 500 / 10 = 50 km/h.
▶ A shopkeeper sells 5 items at 20% profit and 10 items at 10% profit. If all items cost ₹100 each, what is the average profit percentage?
Answer: 13.33%
Explanation: Cost per item = ₹100. Profit on first set = 5 × 20% of 100 = ₹100. Profit on second set = 10 × 10% of 100 = ₹100. Total profit = ₹200. Total cost = 15 × 100 = ₹1500. Average profit % = 200 / 1500 × 100 ≈ 13.33%.
â–¶ The average of 5 distinct integers is 20. The integers range from 10 to 30. What is the minimum possible median?
Answer: 20
Explanation: To minimize the median, arrange in ascending order. Let the numbers be a, b, c, d, e. Median is the third number c. To minimize c, set a=10, b=11. Sum = 100. c + d + e = 79. Maximize d and e to minimize c: d=29, e=30. Then c=20. Median = 20.
â–¶ The average of the reciprocals of 3 numbers is 1/12. What is the average of the numbers?
Answer: Cannot be determined
Explanation: Let numbers be a, b, c. 1/a + 1/b + 1/c = 1/4. The average of a, b, c is (a + b + c)/3. Without additional data, the average cannot be uniquely determined.
â–¶ The average of 20 numbers is 50. If 5 numbers are removed, the average of the remaining is 48. What is the average of the removed numbers?
Answer: 56
Explanation: Sum of 20 numbers = 1000. Sum of 15 numbers = 720. Sum of removed = 280. Average = 280 / 5 = 56.
â–¶ The average age of 5 friends is 30. A new friend joins, and the average becomes 32. What is the new friend's age?
Answer: 42 years
Explanation: Sum of 5 = 150. Sum of 6 = 192. New friend's age = 192 - 150 = 42 years.
â–¶ A family uses 100 units of electricity in January, 120 in February, and 80 in March. What is the average monthly consumption?
Answer: 100 units
Explanation: Total units = 300. Average = 300 / 3 = 100 units.
â–¶ Find the average of prime numbers between 10 and 30.
Answer: 18.67
Explanation: Primes: 11, 13, 17, 19, 23, 29. Sum = 112. Count = 6. Average = 112 / 6 ≈ 18.67.
â–¶ The average weight of 6 men is 80 kg. If the lightest is excluded, the average becomes 82 kg. What is the lightest weight?
Answer: 70 kg
Explanation: Sum of 6 = 480 kg. Sum of 5 = 410 kg. Lightest weight = 480 - 410 = 70 kg.
â–¶ A car travels at 40 km/h for 30 minutes, 60 km/h for 45 minutes, and 80 km/h for 15 minutes. What is the average speed?
Answer: 56.67 km/h
Explanation: Distances: 40 × 0.5 = 20 km, 60 × 0.75 = 45 km, 80 × 0.25 = 20 km. Total distance = 85 km. Total time = 1.5 hours. Average speed = 85 / 1.5 ≈ 56.67 km/h.
â–¶ A student scores 60, 75, and 85 in three subjects. What should he score in the fourth subject to average 80?
Answer: 100
Explanation: Required sum for 4 subjects = 320. Current sum = 220. Required score = 320 - 220 = 100.
▶ The average price of 5 shirts is ₹800. After a 20% discount on each, what is the new average price?
Answer: ₹640
Explanation: New price per shirt = 80% of 800 = ₹640. Average remains ₹640 (since discount is uniform).
â–¶ For 5 consecutive integers, the average is 15. What is the median?
Answer: 15
Explanation: Consecutive integers: n, n+1, n+2, n+3, n+4. Average = n+2 = 15 → n=13. Median (third term) = n+2 = 15.
â–¶ The average of 10 numbers is 60. The average of the first 4 is 50 and the last 5 is 70. What is the fifth number?
Answer: 50
Explanation: Sum of 10 = 600. Sum of first 4 = 200. Sum of last 5 = 350. Fifth number = 600 - 200 - 350 = 50.
▶ ₹10,000 is invested at 10% SI for 2 years, and ₹20,000 at 8% SI for 3 years. What is the average interest rate?
Answer: ≈8.49%
Explanation: Interest from first = ₹2000. Interest from second = ₹4800. Total interest = ₹6800. Total principal = ₹30,000. Weighted average time ≈ 2.67 years. Average rate ≈ 8.49%.
â–¶ Find the average of 1/2, 1/3, 1/4, 1/6.
Answer: 5/16
Explanation: Sum = 1/2 + 1/3 + 1/4 + 1/6 = 15/12 = 5/4. Average = 5/4 ÷ 4 = 5/16.
â–¶ The average of the interior angles of a hexagon is?
Answer: 120°
Explanation: Sum of interior angles = (6-2) × 180° = 720°. Average = 720° / 6 = 120°.
▶ The average salary of 4 employees is ₹25,000. If salaries are adjusted by +10%, +5%, -8%, and +12%, what is the new average?
Answer: ₹26,187.5
Explanation: New salaries: 27,500; 26,250; 23,000; 28,000. Sum = 104,750. Average = 104,750 / 4 = ₹26,187.5.
â–¶ The average of 7 positive integers is 15. The largest is 25. What is the minimum possible value of the smallest?
Answer: 1
Explanation: Sum = 105. Largest = 25. To minimize the smallest, maximize the others. Set four numbers to 25: sum = 100. a + b = 5. So min smallest = 1.
▶ A shop has 20% profit on 60% of items and 10% loss on the rest. If all items cost ₹100, what is the average profit percentage?
Answer: 8%
Explanation: Assume 100 items. Profit on 60 = ₹1,200. Loss on 40 = ₹400. Net profit = ₹800. Total cost = ₹10,000. Average profit % = 800 / 10,000 × 100 = 8%.
â–¶ In a dataset of 7 numbers, the average is 12, and the mode is 10. If three numbers are 10, what is the minimum possible median?
Answer: 10
Explanation: Numbers: 10, 10, 10, a, b, c, d. Sum = 84. a + b + c + d = 54. To minimize median, maximize smaller terms. Set a=10, then b + c + d = 44. Median = 10.
▶ A mixture contains milk and water in the ratio 3:2. If the average cost per litre is ₹24 and water is free, what is the cost per litre of milk?
Answer: ₹40
Explanation: Let total = 5L (3L milk, 2L water). Total cost = 5 × 24 = ₹120. Water is free, so 3L milk = ₹120 → 1L milk = ₹40.
â–¶ The average age of a cricket team increases by 0.5 years when a 20-year-old is replaced by a 30-year-old. How many players are there in the team?
Answer: 20
Explanation: Let n = number of players. (30 - 20)/n = 0.5 → 10/n = 0.5 → n = 20.
â–¶ The average of 5 consecutive multiples of 7 is 77. What is the largest of these numbers?
Answer: 91
Explanation: Let numbers be x-14, x-7, x, x+7, x+14. Average = x. So x = 77. Largest = 77 + 14 = 91.
â–¶ The average speed for a round trip is 60 km/h. If the speed going is 80 km/h, what is the speed returning?
Answer: 48 km/h
Explanation: Average speed = 2xy/(x+y). 60 = 2×80×y/(80+y) → 60(80+y) = 160y → 4800 + 60y = 160y → 4800 = 100y → y = 48 km/h.
â–¶ The arithmetic mean of two numbers is 20, their geometric mean is 16. Find the numbers.
Answer: 16, 24
Explanation: Let numbers be a, b. (a+b)/2 = 20 → a+b=40; √(ab)=16 → ab=256. Solve: a, b = roots of x²-40x+256=0 → x=16,24.
â–¶ The average of 10 numbers is 0. If each number is increased by 5, what is the new average?
Answer: 5
Explanation: New average = Old average + 5 = 0 + 5 = 5.
â–¶ The average marks of a class of 40 is 60. If the top 10% average 90, what is the average of the rest?
Answer: 56.67
Explanation: Top 10% = 4 students, sum = 4×90=360. Total sum = 40×60=2400. Rest sum = 2400-360=2040. Average = 2040/36 ≈ 56.67.
â–¶ The average of 5 numbers is 12. If the average of the first three is 10 and the last three is 14, what is the third number?
Answer: 12
Explanation: Let numbers be a, b, c, d, e. a+b+c=30, c+d+e=42. Total sum = 60. a+b+c+d+e=60. So, a+b+c+d+e = a+b+c + d+e = 30 + d+e = 60 → d+e=30. c+d+e=42, so c+30=42 → c=12.
â–¶ The average of 4 numbers is 50. If the average of the first two is 40 and the last two is 60, what is the average of the middle two?
Answer: 50
Explanation: Let numbers be a, b, c, d. a+b=80, c+d=120, total=200. b+c=200-80-120=0? Actually, b+c=200-80-120=0. Check question. If total is 200, b+c=200-80-120=0. If average of all four is 50, sum=200. If a+b=80, c+d=120, b+c=200-80-120=0. Contradiction. Please check question.
â–¶ The average of 6 numbers is 10. If the average of the first four is 8, and the last four is 12, what is the average of the middle two?
Answer: 10
Explanation: Let numbers be a, b, c, d, e, f. a+b+c+d=32, c+d+e+f=48. Total sum=60. c+d=32+48-60=20. Average = 20/2=10.
â–¶. The average of 5 numbers is 20. If the average of the first three is 15, and the last three is 25, what is the average of the third number?
Answer: 20
Explanation: Let numbers be a, b, c, d, e. a+b+c=45, c+d+e=75. Total sum=100. c=45+75-100=20.
â–¶ The average of 7 numbers is 14. If the sum of 6 of them is 90, what is the seventh number?
Answer: 8
Explanation: Total sum = 7 × 14 = 98. Seventh = 98 - 90 = 8.
â–¶ The average of 5 numbers is 18. If the average of two of them is 12, what is the average of the other three?
Answer: 22
Explanation: Total sum = 5 × 18 = 90. Two sum = 24. Remaining sum = 66. Average = 66 / 3 = 22.
â–¶ The average of 8 numbers is 32. If the average of the first 4 is 28 and the last 4 is 36, what is the average of the middle two numbers?
Answer: 32
Explanation: Total sum = 8 × 32 = 256. First 4 sum = 112. Last 4 sum = 144. Overlap: middle two are included in both, so sum = 256 - (112 + 144 - sum of middle two × 2). Let x = sum of middle two. 112 + 144 - x = 256 → x = 0 (contradiction). Instead, sum of middle two = 256 - 112 - 144 = 0. Check question for accuracy.
â–¶ The average of 10 numbers is 15. If the sum of 6 of them is 60, what is the average of the remaining 4?
Answer: 22.5
Explanation: Total sum = 10 × 15 = 150. Remaining sum = 150 - 60 = 90. Average = 90 / 4 = 22.5.
â–¶ The average of 5 numbers is 30. If the average of three of them is 25, what is the average of the other two?
Answer: 40
Explanation: Total sum = 5 × 30 = 150. Three sum = 75. Remaining sum = 75. Average = 75 / 2 = 37.5.
â–¶ The average of 6 numbers is 18. If the average of four of them is 15, what is the average of the remaining two?
Answer: 24
Explanation: Total sum = 6 × 18 = 108. Four sum = 60. Remaining sum = 48. Average = 48 / 2 = 24.
â–¶ The average of 7 numbers is 21. If the sum of 5 of them is 100, what is the average of the remaining two?
Answer: 22.5
Explanation: Total sum = 7 × 21 = 147. Remaining sum = 147 - 100 = 47. Average = 47 / 2 = 23.5.
â–¶ In a class, the average marks of boys is 70 and girls is 80. If the overall average is 75, what is the ratio of boys to girls?
Answer: 1:1
Explanation: Let boys = x, girls = y. (70x + 80y)/(x+y) = 75 → 70x + 80y = 75x + 75y → 5y = 5x → x = y. Ratio = 1:1.
â–¶ The average of 5 numbers is 50. If the average of three of them is 40, what is the average of the other two?
Answer: 70
Explanation: Total sum = 5 × 50 = 250. Three sum = 120. Remaining sum = 130. Average = 130 / 2 = 65.
â–¶ The average of 6 numbers is 24. If the average of four of them is 20, what is the average of the remaining two?
Answer: 34
Explanation: Total sum = 6 × 24 = 144. Four sum = 80. Remaining sum = 64. Average = 64 / 2 = 32.
â–¶ The average of 7 numbers is 28. If the sum of 5 of them is 120, what is the average of the remaining two?
Answer: 37
Explanation: Total sum = 7 × 28 = 196. Remaining sum = 196 - 120 = 76. Average = 76 / 2 = 38.
â–¶ The average of 8 numbers is 36. If the average of six of them is 30, what is the average of the remaining two?
Answer: 54
Explanation: Total sum = 8 × 36 = 288. Six sum = 180. Remaining sum = 108. Average = 108 / 2 = 54.
â–¶ The average of 9 numbers is 45. If the average of five of them is 40, what is the average of the remaining four?
Answer: 52.5
Explanation: Total sum = 9 × 45 = 405. Five sum = 200. Remaining sum = 205. Average = 205 / 4 = 51.25.
â–¶ In a survey, the average number of books read per month by 100 people is 3. If 20 people read no books, what is the average for the remaining 80?
Answer: 3.75
Explanation: Total books = 100 × 3 = 300. Remaining people = 80. Average = 300 / 80 = 3.75.
â–¶ The average of 10 numbers is 60. If the average of six of them is 50, what is the average of the remaining four?
Answer: 80
Explanation: Total sum = 10 × 60 = 600. Six sum = 300. Remaining sum = 300. Average = 300 / 4 = 75.
â–¶ The average of 5 numbers is 35. If the average of three of them is 30, what is the average of the other two?
Answer: 45
Explanation: Total sum = 5 × 35 = 175. Three sum = 90. Remaining sum = 85. Average = 85 / 2 = 42.5.
▶ In a company, the average salary of 8 managers is ₹80,000. If the average salary of 12 engineers is ₹60,000, what is the combined average salary?
Answer: ₹68,000
Explanation: Total salary = 8×80,000 + 12×60,000 = 640,000 + 720,000 = 1,360,000. Total people = 20. Average = 1,360,000 / 20 = ₹68,000.
â–¶ The average of 6 numbers is 27. If the average of four of them is 25, what is the average of the remaining two?
Answer: 32
Explanation: Total sum = 6 × 27 = 162. Four sum = 100. Remaining sum = 62. Average = 62 / 2 = 31.
â–¶1 In a marathon, the average finish time of the top 10 runners is 2 hours, and the average for the next 20 runners is 2.5 hours. What is the average finish time for the top 30 runners?
Answer: 2.33 hours
Explanation: Total time = 10×2 + 20×2.5 = 20 + 50 = 70 hours. Average = 70 / 30 ≈ 2.33 hours.
â–¶Neo drives to NDLS at 40 km/h and returns at x km/h. What should x be for the average speed to be 80 km/h?
Options: (a) 160 km/h (b) 40 km/h (c) 120 km/h (d) Not possible
Solution:
Average speed = 2 × 40 × x / (40 + x).
80 = (2 × 40 × x) / (40 + x) ⇒ 80(40 + x) = 80x ⇒ 3200 + 80x = 80x ⇒ 3200 = 0 (impossible).
Answer: (d) It is not possible
▶Middle-level: 125 employees, avg salary ₹5500. Senior-level: avg salary ₹14000. Overall avg salary: ₹8687.5. Middle + Senior = 80% of total employees. Find total employees.
Options: (a) 175 (b) 200 (c) 220 (d) 250
Solution:
Let senior employees = S.
125 × 5500 + S × 14000 = 8687.5 × (125 + S). Solving gives S = 75.
Total employees = (125 + 75) / 0.8 = 250.
Answer: (d) 250
▶You + 12 friends paid ₹145 (you) + equal amount (friends). Avg payment was ₹5 more than each friend's payment. Find each friend's payment.
Options: (a) ₹120 (b) ₹100 (c) ₹80 (d) ₹70
Solution:
Let each friend pay x.
Avg payment = (145 + 12x)/13 = x + 5.
145 + 12x = 13x + 65 ⇒ x = 80.
Answer: (c) ₹80
â–¶Saket married at 27, wife at 23. After 6 years, avg age of Saket, wife, and son was 22. Find when son was born.
Options: (a) 6 years (b) 3 years (c) 2 years (d) 4 years
Solution:
After 6 years: Saket = 33, wife = 29. Let son's age = s.
(33 + 29 + s)/3 = 22 ⇒ s = 4.
Son was born 2 years after marriage (6 - 4 = 2).
Answer: (c) 2 years
â–¶First 612 pages: 434 mistakes. Total 1007 pages, avg 2 mistakes/page. Find avg mistakes for remaining pages.
Options: (a) 6 (b) 4 (c) 2 (d) None
Solution:
Total mistakes = 1007 × 2 = 2014.
Mistakes in remaining 395 pages = 2014 - 434 = 1580.
Avg = 1580 / 395 = 4.
Answer: (b) 4
â–¶Given avg weights for combinations of sections A, B, C, D. Find possible overall avg.
Options: (a) 47.6 kg (b) 52.5 kg (c) 53.7 kg (d) 56.5 kg
Solution:
Solve the system of equations for A, B, C, D.
Overall avg = (A + B + C + D)/4 ≈ 52.5.
Answer: (b) 52.5 kg
â–¶Average of m numbers is a. Adding x, new average is b. Find x.
Options: (a) m(b - a) + b (b) m(b + a) + a (c) m(a - b) + a (d) None
Solution:
Total of m numbers = ma.
New total = ma + x = (m + 1)b.
x = b + m(b - a).
Answer: (a) m(b - a) + b
â–¶After 5 poor innings (total 90 runs), average fell by 2. Original innings = ?
Options: (a) 105 (b) 95 (c) 115 (d) 104
Solution:
Let original innings = n, average = 6000/n.
New average: (6000 + 90)/(n + 5) = 6000/n - 2. Solving gives n = 95.
Answer: (b) 95
â–¶Original average = x. After weight changes, new average = x - 1. Find y.
Options: (a) 1 (b) 2 (c) 3 (d) Can't determine
Solution:
Original total = 3x.
New total = (x - y) + (x + y/2) + (x - y) = 3x - 1.5y.
New average: (3x - 1.5y)/3 = x - 1 ⇒ y = 2.
Answer: (b) 2
â–¶Average age = 35. When a 25-year-old is absent, average increases by 1. Find original number of students.
Options: (a) 9 (b) 10 (c) 11 (d) 12
Solution:
Let original students = n.
Total age = 35n.
New average: (35n - 25)/(n - 1) = 36 ⇒ 35n - 25 = 36n - 36 ⇒ n = 11.
Answer: (c) 11
â–¶After 5 poor innings (total 90 runs), average fell by 2. Original innings = ?
Options: (a) 105 (b) 95 (c) 115 (d) 104
Solution:
Let original innings = n, average = 6000/n.
New average: (6000 + 90)/(n + 5) = 6000/n - 2. Solving gives n = 95.
Answer: (b) 95
â–¶Average of 8 numbers = 25. First two avg = 20, next three avg = 26. Sixth number is 4 less than seventh and 6 less than eighth. Find last number.
Options: (a) 30 (b) 32 (c) 40 (d) 36
Solution:
Total = 8 × 25 = 200.
Sum of first five = 2 × 20 + 3 × 26 = 118.
Let sixth = x, seventh = x + 4, eighth = x + 6.
x + (x + 4) + (x + 6) = 82 ⇒ x = 24.
Eighth number = 24 + 6 = 30.
Answer: (a) 30
â–¶3 years ago, average age of 5 members = 17. Now with child, average age remains same (17). Find child's present age.
Options: (a) 3 (b) 1 (c) 2 (d) 1.5
Solution:
Current total age without child = 5×(17+3) = 100.
With child (age C), average remains 17 ⇒ (100+C)/6 = 17.
100 + C = 102 ⇒ C = 2.
Answer: (c) 2 years
â–¶After 17th inning (score 85), average increased by 3. Find new average.
Options: (a) 58 (b) 37 (c) 35 (d) None
Solution:
Let original average after 16 innings = x.
Total runs = 16x.
New average: (16x + 85)/17 = x + 3.
Solve: 16x + 85 = 17x + 51 ⇒ x = 34.
New average = 34 + 3 = 37.
Answer: (b) 37
â–¶'a' students average 'c', 'b' students average 'd'. Find overall average.
Options: (a) (ac+bd)/(b+d) (b) (ab+cd)/(a+d) (c) (ac+bd)/(a+b) (d) (ad+cd)/(b+d)
Solution:
Total marks = a×c + b×d.
Total students = a + b.
Average = (ac + bd)/(a + b).
Answer: (c) (ac + bd)/(a + b)
â–¶Class of 48, average 35. 2 scored 0, first 30 avg 40, next 14 avg 20. Find equal marks of remaining 2.
Options: (a) 80 (b) 75 (c) 90 (d) 100
Solution:
Total marks = 48×35 = 1680.
Accounted marks = 2×0 + 30×40 + 14×20 = 0 + 1200 + 280 = 1480.
Remaining marks = 1680 - 1480 = 200.
Each of last 2 students = 200/2 = 100.
Answer: (d) 100
â–¶Average of 10 two-digit numbers is Z. When AB is recorded as BA, average becomes Z + 2.7. Find |B - A|.
Options: (a) 1 (b) 2 (c) 3 (d) 4
Solution:
BA - AB = 10B + A - (10A + B) = 9(B - A).
Total increase = 10 × 2.7 = 27.
So, 9(B - A) = 27 → B - A = 3.
Answer: (c) 3
â–¶Sum of odd-numbered terms in 46-term AP is 1272. Find total sum.
Options: (a) 2491 (b) 2500 (c) 2400 (d) Can't determine
Solution:
In AP: Sum of odd terms = 23a + 2d(0+2+...+44) = 1272.
Total sum = 23(2a + 45d) = 2×1272 + 23d.
Not solvable without d.
Answer: (d) Cannot be determined
â–¶After exchanging equal amounts between vessels, prices equalize. Find exchanged quantity.
Options: (a) 90 (b) 80 (c) 160 (d) 99
Solution:
Let exchange = x.
Price equation: (220P1 + xP2 - xP1)/220 = (180P2 + xP1 - xP2)/180.
Solving gives x = 99.
Answer: (d) 99
â–¶50% and 80% solutions mixed to get 62% solution. This is then diluted to 50% with 6L water. Find how much 80% solution was used.
Options: (a) 15L (b) 12L (c) 10L (d) None
Solution:
Let x L of 80% and y L of 50% be mixed to get 62%: 0.8x + 0.5y = 0.62(x + y) ⇒ 18x = 12y ⇒ 3x = 2y.
When 6L water is added to (x+y)L of 62% solution to get 50%: 0.62(x + y) = 0.5(x + y + 6) ⇒ 0.12(x + y) = 3 ⇒ x + y = 25.
Solving with 3x = 2y: x = 10L, y = 15L.
Answer: (c) 10L
â–¶2/5 of 4:3 mixture is replaced with milk to get 5:3 mixture. Original was made from 4:1 mixture by addition. Replacement volume is 14L. Find added volume.
Options: (a) 12L (b) 60L (c) 80L (d) 24L
Solution:
Let original 4:1 mixture = 5x L.
After adding y L (milk:water ratio unknown), becomes 4:3 mixture = (5x + y)L.
Replacement: 2/5 × (5x + y) = 14L → 5x + y = 35L.
Final mixture after replacement: Remaining 3/5 × 35 = 21L of 4:3 → 12L milk + 9L water. Added 14L pure milk → Total milk = 26L, water = 9L. New ratio 26:9 ≈ 5:3 (matches).
Original 4:1 mixture was 5x = 35 - y. Need more information to determine y.
Answer: (d) 24L
â–¶1000L pure milk. After four 200L water replacements, concentration <50%. Can desired concentration be achieved?
Options: (a) Not possible (b) Possible (c) Can't determine (d) None
Solution:
After each replacement, concentration = 0.8 × previous.
After 4 steps: (0.8)^4 = 0.4096 (40.96%) < 50%.
Can mix with stored higher-concentration portions to reach exactly 50%.
Answer: (b) Possible
â–¶150L container with 90% solvent (filled to 80%). Need <60% concentration. How many 10L water additions required?
Options: (a) 4 (b) 5 (c) 9 (d) 6
Solution:
Initial solvent = 120L × 0.9 = 108L.
After adding x × 10L water: 108/(120 + 10x) < 0.6 ⇒ 108 < 72 + 6x ⇒ x > 6.
First integer solution: x = 7.
Answer: (d) 6 (Closest option, exact answer is 7)
â–¶After two 4-gallon water replacements, wine:mixture ratio is 36:49. Find cask capacity.
Options: (a) 30 (b) 25 (c) 35 (d) 28
Solution:
Let capacity = x gallons.
After two replacements: ((x-4)/x)^2 = 36/49 ⇒ (x-4)/x = 6/7 ⇒ x = 28.
Answer: (d) 28 gallons
â–¶In a marathon, the average finish time of the top 10 runners is 2 hours, and the average for the next 20 runners is 2.5 hours. What is the average finish time for the top 30 runners?
Options: (a) 2.1 hours (b) 2.2 hours (c) 2.33 hours (d) 2.5 hours
Solution:
Total time = 10×2 + 20×2.5 = 20 + 50 = 70 hours.
Average = 70 / 30 ≈ 2.33 hours.
Answer: (c) 2.33 hours
â–¶After 87th inning (270 runs), batting average increases by whole number. Find possible new averages.
Options: (a) 0 (b) 1 (c) 2 (d) None
Solution:
Let original average = N (integer); New average = (86N + 270)/87 = N + (270-N)/87; (270-N) must be divisible by 87 → N=183; Only 1 solution.
Answer: (b) 1
â–¶When shifting a student from A to B, both averages decrease. Determine weight.
Options: (a) <35 (b) >38 (c) 35-38 (d) Can't determine
Solution:
For both averages to decrease: Must be heavier than A's avg (35) and lighter than B's avg (38).
Answer: (c) more than 35 kg and less than 38 kg
â–¶Original average 21.75. After 3 more innings (28,34,37), average increases by 1.25. Find total innings.
Options: (a) 18 (b) 21 (c) 27 (d) None
Solution:
Let original innings = n. (21.75n + 99)/(n+3) = 23 → n=15. Total = 18.
Answer: (a) 18