Average
- The average of five consecutive odd numbers is 47. What is the largest of these numbers? Answer: B. 51 Answer: (B) 51 For consecutive odd numbers the average is the middle number, 47. The numbers are 43, 45, 47, 49, 51, so the la... 1
- The average of 11 numbers is 36. The average of the first six numbers is 32 and that of the last six numbers is 40. What is the sixth number? Answer: D. 36 Answer: (D) 36 The 6th number is counted in both groups. Sixth = 6 × 32 + 6 × 40 - 11 × 36 = 192 + 240 - 396 = 36 . 1
- The average age of 30 students in a class is 14 years. When the teacher's age is included, the average becomes 15 years. What is the teacher's age? Answer: B. 45 years Answer: (B) 45 years Teacher's age = 31 × 15 - 30 × 14 = 465 - 420 = 45 years. 1
- The average weight of 20 students is 45 kg. When the teacher's weight is included, the average increases by 1 kg. What is the teacher's weight (in kg)? Answer: B. 66 Answer: (B) 66 New total = 21 × 46 = 966 kg; old total = 900 kg. Teacher = 66 kg. 1
- The average of five numbers is 42. When one number is removed, the average of the remaining four numbers becomes 40. What is the number removed? Answer: D. 50 Answer: (D) 50 Sum of five = 210, sum of four = 160. Removed number = 210 − 160 = 50. 1
- The average of 13 results is 40. The average of the first seven is 38 and the average of the last seven is 43. What is the seventh result? Answer: A. 47 Answer: (A) 47 The seventh result is counted in both groups of seven. Seventh = 7 × 38 + 7 × 43 − 13 × 40 = 266 + 301 − 520 =... 1
- A car goes from P to Q at 40 km/h and returns from Q to P at 60 km/h. What is its average speed for the whole journey? Answer: A. 48 km/h Answer: (A) 48 km/h Shortcut: for equal distances, average speed = 2xy/x+y = 2 × 40 × 60/100 = 48 km/h. Trap: 50 km/h is... 1
- The average of 50 numbers is 38. If two numbers, 45 and 55, are removed, what is the average of the remaining numbers? Answer: B. 37.5 Answer: (B) 37.5 Sum of 50 = 1900. Remaining sum = 1900 − 100 = 1800. Average = 1800 ÷ 48 = 37.5. 1
- The average marks of 40 students were found to be 60. Later it was found that one student's mark of 85 had been entered as 58. What is the correct average? Answer: B. 60.675 Answer: (B) 60.675 Shortcut: the total was short by 85 − 58 = 27, so the average rises by 27 ÷ 40 = 0.675. Correct average... 1
- A batsman scores 96 runs in his 19th innings, and this raises his average by 4. What is his average after the 19th innings? Answer: D. 24 Answer: (D) 24 Shortcut: new average = runs in this innings − (old innings × rise) = 96 − 18 × 4 = 24. Plain: let the old aver... 1
- The average of three numbers is 77. The first number is twice the second, and the second is twice the third. What is the first number? Answer: C. 132 Answer: (C) 132 Let the third be x. Then the second is 2x and the first is 4x. 7x = 3 × 77 = 231, so x = 33. First number = 4... 1
- Section A has 30 students with average marks 65, and section B has 20 students with average marks 70. What is the average of all 50 students? Answer: B. 67 Answer: (B) 67 Combined average = 30 × 65 + 20 × 70/50 = 3350/50 = 67 . Shortcut: the answer lies closer to 65 because section... 1
- The average monthly income of a family with four earning members was ₹15,000. When one of them retired and stopped earning, the average income of the remaining three became ₹13,000. What was the income of the member who retired? Answer: A. ₹21,000 Answer: (A) ₹21,000 4 × 15,000 − 3 × 13,000 = 60,000 − 39,000 = ₹21,000. 1
- The average weight of 8 people rises by 2.5 kg when a new person takes the place of one who weighs 65 kg. What is the weight of the new person? Answer: A. 85 kg Answer: (A) 85 kg Shortcut: new person = person replaced + (number of people × rise) = 65 + 8 × 2.5 = 85 kg. 1
- What is the average of the first ten multiples of 7? Answer: A. 38.5 Answer: (A) 38.5 Average = 7 × (average of 1 to 10) = 7 × 5.5 = 38.5. 1
- The average temperature from Monday to Wednesday was 36°C and from Tuesday to Thursday was 34°C. Thursday's temperature was \(\frac{4}{5}\) of Monday's. What was Thursday's temperature? Answer: D. 24°C Answer: (D) 24°C Mon + Tue + Wed = 108 and Tue + Wed + Thu = 102, so Mon − Thu = 6. Mon − 0.8 Mon = 6 gives Mon = 30°C, so T... 1
- The average of 21 results is 20. The average of the first 10 is 17 and the average of the last 10 is 21. What is the 11th result? Answer: C. 40 Answer: (C) 40 Total = 21 × 20 = 420. First 10 = 170, last 10 = 210. 11th result = 420 − 170 − 210 = 40. 1
- The average of five consecutive odd numbers A, B, C, D and E (in increasing order) is 45. What is the product of B and D? Answer: C. 2021 Answer: (C) 2021 The middle number C equals the average, 45. So B = 43 and D = 47. B × D = 43 × 47 = (45 − 2)(45 + 2) = 2025... 1
- The average age of a husband and wife was 26 years when they married. Six years later they have a two-year-old child. What is the average age of the family now? Answer: C. 22 years Answer: (C) 22 years At marriage the couple's total age = 52. After 6 years it is 52 + 12 = 64. Family total = 64 + 2 =... 1
- The average weight of A, B and C is 45 kg. The average weight of A and B is 40 kg and that of B and C is 43 kg. What is B's weight? Answer: D. 31 kg Answer: (D) 31 kg A + B + C = 135, A + B = 80 and B + C = 86. B = (A + B) + (B + C) − (A + B + C) = 80 + 86 − 135 = 31 kg. 1
- The average marks of 30 students in a test is 40. The average of those who passed is 45 and the average of those who failed is 30. How many students passed? Answer: B. 20 Answer: (B) 20 Shortcut (alligation): passed : failed = (40 − 30) : (45 − 40) = 10 : 5 = 2 : 1. Passed = 2/3 × 30 = 20 . Plain... 1
- What is the average of 12, 18, 25, 31 and 44? Answer: D. 26 Answer: (D) 26 Sum = 130, so average = 130 ÷ 5 = 26. 1
- What is the average of the first 20 natural numbers? Answer: B. 10.5 Answer: (B) 10.5 Shortcut: average of 1 to n = n+1/2 = 21/2 = 10.5 . 1
- What is the average of the first 15 odd natural numbers? Answer: C. 15 Answer: (C) 15 Shortcut: the average of the first n odd numbers is n. So the answer is 15. Plain: sum = 15² = 225, and 225 ÷ 1... 1