SSC CGL Pre + Mains 2023 Average Questions PDF

## SSC CGL PRE + MAINS - 2023 **[Average | Number Based] Type: 04** 1. The average of six numbers is 45.5. If a new number is added then the new average becomes 47. Find the new number? - (A) 62 - (B) 56 - (C) 54 - (D) 52 2. The mean of 11 numbers is 182. If the mean of first 6 n...

## SSC CGL PRE + MAINS - 2023 **[Average | Number Based] Type: 04** 1. The average of six numbers is 45.5. If a new number is added then the new average becomes 47. Find the new number? - (A) 62 - (B) 56 - (C) 54 - (D) 52 2. The mean of 11 numbers is 182. If the mean of first 6 numbers is 199 that of the last 6 numbers is 161. Find the sixth number. - (A) 79 - (B) 118.5 - (C) 158 - (D) 237 3. The mean of 19 numbers is 111. If the mean of first 10 numbers is 82 and that of the last 10 numbers is 129. Find the 10th number. - (A) 0 - (B) 82 - (C) 1 - (D) 2 4. Average of 11 numbers is 36, whereas average of 9 of them is 34. If the remaining two numbers are in the ratio of 2:3, find the value of the smallest number (between remaining two numbers). - (A) 54 - (B) 36 - (C) 45 - (D) 48 5. The average of 28 numbers is 77. The average of first 14 numbers is 74 and the average of last 15 numbers is 84. If the 14th number is excluded, then what is the average of remaining numbers? (correct to one decimal places) - (A) 73.1 - (B) 74.7 - (C) 77 - (D) 76.9 6. There are 6 consecutive odd numbers. The difference between the square of the average age of the last three numbers and that of first three numbers is 288. What is the largest odd number? - (A) 31 - (B) 27 - (C) 29 - (D) 25 7. Three numbers are such that, first number is double than that of second and half of third number. If the average of all three numbers is 56, then what is the difference between first and third number? - (A) 24 - (B) 48 - (C) 42 - (D) 14 8. The average of _n_ numbers is 42. If 75% of the numbers are increased by 4 each and the remaining numbers are decreased by 8 each, then what is the average of the numbers, so obtained? - (A) 43.8 - (B) 43 - (C) 42.5 - (D) 44 9. The average of three numbers is 60. If first number is equal to 1/4 times of the sum of other two numbers, then what is the first number? - (A) 36 - (B) 63 - (C) 32 - (D) 34 10. The numbers 2, 3, 4 and 5 occur (2+5k), (5k-7), (2k-3) and (k+2) times, respectively. The average of the numbers is 2.85. Later on, the number 2 was replaced by 6 in all the places. What is the average of the new numbers? - (A) 2.4 - (B) 4.75 - (C) 3.85 - (D) 5.25 11. The average of first five numbers is three times than that of the sixth number. If the average of all six numbers is 10 then what is the value of sixth number? - (A) 6 - (B) 4 - (C) 15 - (D) 9 12. The average of 11 numbers is 10.8. If the average of first 6 numbers is 10.4 and the average of last 6 numbers is 11.5. Then find out the middle (6th) number? - (A) 10.3 - (B) 12.6 - (C) 13.5 - (D) 15.5 13. The average of 20 numbers is 12. If the average of first 12 numbers is 11 and the average of next 7 numbers is 10. Then find out the last number? - (A) 40 - (B) 38 - (C) 48 - (D) 50 14. The average of 8 numbers is 20. From these 8 numbers, the average of first 3 numbers is 15 and next 2 numbers is 25. If sixth number is 4 less than that of seventh number and 7 less than that of eighth number, then what is the last number? - (A) 25 - (B) 18 - (C) 21 - (D) 27 15. The average of eleven numbers is 68. The average of the first four numbers is 78 and that of the next four numbers is 63. The 9th number is two times the 11th number and the 10th number is 4 less than the 11th number. What is the average of the 9th and 11th numbers? - (A) 72.6 - (B) 70.1 - (C) 72.2 - (D) 70.5 16. The average of 8 numbers is 20. The average of first two numbers is 15 and that of the next three is 21. If the sixth number be less than the seventh and eight numbers by 4 and 7 respectively, then the eighth number is: - (A) 18 - (B) 22 - (C) 25 - (D) 27 17. The average of twelve number is 39. The average of the last five numbers is 35, and that of the first four number is 40. The fifth number is 6 less than the sixth number and 5 more than the seventh number. The average of the fifth and sixth number is : 18. The average of twenty-five numbers is 54. The average of the first 13 numbers and that of the last 13 numbers is 52.8 and 62.2 respectively. If the 13th number is excluded, then what is the average of the remaining numbers (correct to one decimal place) ? - (A) 51.2 - (B) 49.8 - (C) 50.2 - (D) 50.6 19. The average of twelve numbers is 45.5. The average of the first four numbers is 41.5 and that of the next five numbers is 48. The 10th number is 4 more than the 11th number and 9 more than the 12th number. What is the average of the 10th and 12th numbers? - (A) 46.5 - (B) 47 - (C) 46 - (D) 47.8 20. The average of three numbers a, b and c is 2 more than c. The average of a and b is 48. If d is 10 less than c, then the average of c and d is: - (A) 36 - (B) 40 - (C) 38 - (D) 35 21. S₁ is an ascending series of 5 positive numbers, where in the difference between two consecutive numbers of S₁ is 3. The lowest number of S₁ is 13. If the 2nd highest number of S₁ is 2 more than the lowest number of another series of 4 consecutive positive numbers (S₂), what is the average of S₂? - (A) 21.5 - (B) 26 - (C) 22.5 - (D) 23 22. The average of twelve number is 39. The average of the last five numbers is 35, and that of the first four number is 40. The fifth number is 6 less than the sixth number and 5 more than the seventh number. The average of the fifth and sixth number is : - (A) 39 - (B) 50 - (C) 44 - (D) 47 **Solution** 1. (B) Average of 6 Numbers = 45.5 - If one New Number add then avg. = 47 - 7th Number = 45.5 + 1.5 × 7 = 56 2. (C) 182 + 6 (199 – 182) – 6 (182 – 161) - 6th Number = 182 + 102 – 126 = 158 3. (C) 19 → 111 ⇒ sum = 2109 - First 10 → 82 ⇒ sum = 820 - Last 10 → 129 sum = 1290 - 10th Number = 1290 + 820 – 2109 = 1 4. (B) Avg of 11 students = 36 ⇒ sum = 396 - 9 Students = 34 ⇒ sum = 306 - A : B = 2 : 3 ⇒ 90/ 5 = 18 5. (B) Total number = 28 × 77 = 2156 - First 14 number total = 14 × 74 = 1036 - Last 15 number total = 15 × 84 = 2296 - 14th number can't two time - rem. total num. 27 = 2156 – 140 = 2016 - Avg. = 2016 / 27 = 74.7 6. (C) 6 consecutive odd numbers - A = 60 × 1/5 = 36 - ⇒ 2x + 1, 2x + 3, 2x + 5, 2x + 7, 2x + 9 and 2x + 11. - (2x + 1 + 2x + 9 + 2x + 11)² / 3 – (2x + 1 + 2x + 3 + 2x + 5)² / 3 = 288 - ⇒ (2x + 9)² – (2x + 3)² = 288 - ⇒ (2x + 9 + 2x + 3) (2x + 9 - 2x – 3) = 288 - ⇒ (4x + 12) × 6 = 288 - ⇒ 4x + 12 = 48 - ⇒ x = 9 - ... Largest odd number = 2x + 11 = 2 × 9 + 11 = 29 7. (B) A = 2 - B = 1 - C = 4 - C – A = 56 × 3 / 7 × 2 = 48 8. (B) Required Average = 42 + 75/100 × 4 – 25/100 × 8 = 42 + 3 – 2 = 43 9. (A) A / (B + C) = 1 / 4 - A = (B + C) / 4 10. (D) Total sum = 2 (2 + 5K) + 3 (5K – 7) + 4 (2K – 3) + 5 (K + 2) - = 38K – 19 - ⇒ 38K – 19 = 2.85 × (2 + 5K + 5K – 7 + 2K – 3 + K + 2) - = 2.85 × (13K – 6) - K = 2 - Number of 2 = 2 + 5 × 2 = 12 times - ATQ, - ⇒ 2 replace by 6 - Now, - 13K – 6 = 13 × 2 – 6 = 20 - Total sum = 6 × 12 + (15K – 2) + (8K – 12) + (5K + 10) - = 72 + (28K – 23) - = 72 + 56 – 2 - = 105 - New avg. = 105 / 20 = 5.25 11. (B) <start_of_image> - A + B + C + .. + F = 15 - F = 1 - 16 ⇒ 64 - F = 14 12. (B) 11 Number avg = 10.8 ⇒ sum = 118.8 - First 6 Number avg. = 10.4 sum = 62.4 - Last 6 Number avg. = 11.5 sum = 69.0 - 6th Number = 131.4 – 118.8 = 12.6 13. (B) 20 → 12 ⇒ sum = 240 - 12 → 11 → sum = 132 - 7 – 10 sum = 70 - Last Number = 240 – 202 = 38 14. (A) 8 → 20 = sum = 20 × 8 = 160 - 3 → 15 = sum = 15 × 3 = 45 - 2 → 25 = sum = 25 × 2 = 50 - 6th Number = x - 7th Number = x + 4 - 8th Number = x + 7 - Now - 95 + x + x + 4 + x + 7 = 160 - 3x + 106 = 160 - 3x = 54 - x = 18 - Last Number = 18 + 7 = 25 15. (D) Avg. devitaion = +10 × 4 – 5 × 4 - = 40 – 20 - = (+)20 - 9th = 2x - 10th = x – 4 - 11th = x - = 68 × 3 – 20 - 4x – 4 = 184 - x = 47 ⇒ 4x = 188 - 10th Number = 2 × 47 = 94 - 11th Number = 47 - Average = (94 + 47) / 2 = 70.5 16. (C) 8 Number avg. = 20 ⇒ Sum = 160 - First 2 Number avg. 15 ⇒ sum 31 - Later 3 Number avg. = 21 → sum 64 - 6th Number = x - 7th Number = x + 4 - 8th Number = x + 7 - Total = 106 + 3x - ATQ - 106 + 3x = 160 - 3x = 54 - x = 18 - Last Number = 18 + 7 = 25 17. (D) Avg of 12 number = 39 ⇒ 39 × 12 = 468 - Avg last five number = 35 ⇒ 35 × 5 = 175 - Avg first four number = 40 4 × 40 = 160 - Let 5th number = x - 6th number = x + 6 - 7th number = x – 5 - 175 + 160 + x + x + 6 + x – 5 = 468 - 335 + 3x + 1 = 468 - 3x = 132 - x = 44 - (5th + 6th) / 2 = (x + x + 6) / 2 = (44 + 44 + 6) / 2 = 47 18. (C) 25th number = 52.8 × 13 + 62.2 × 13 – 25 × 54 = (686.4 + 808.6 – 1350) / 25 = (1495 – 1350) / 25 = 145 - Average 24 Number = (1350 – 145) / 24 = 50.2 19. (A) Average of 12 numbers = 45.5 - Sum = 45.5 × 12 = 546 - Average of first 4 numbers = 41.5 - Sum = 41.5 × 4 = 166 - Average of next 5 numbers = 48 - Sum = 48 × 5 = 240 - Remaining = 546 – 166 – 240 = 140 - 10th 11th 12th - x x - 4 x - 9 - 3x – 13 = 140 - x = 153 / 3 = 51 - Average of 10th and 12th = (51 + 42) / 2 = 46.5 20. (B) - (a + b + c) / 3 = c + 2 - a + b + c – 3c = 6 - a + b + 2c = 6 ….(1) - a + b = 96 ….(2) - c – d = 10 - Eq. (1) & Eq. (2) ... - 90 = 2c - c = 45 ….(4) - Eq. (4) & Eq. (5) ... - d = 35 - Average c and d = (45 + 35) / 2 = 40 21. (A) Number of series S₁ - Þ 13, 16, 19, 22 and 25 - ATQ, - The lowest number of the series S₁ - = 22 – 2 = 20 - Number of series S₁ - ⇒ 20, 21, 22 and 23 - .. Required average - = (20 + 21 + 22 + 23) / 4 = 86 / 4 = 21.5 22. (D) Avg of 12 number = 39 ⇒ 39 × 12 = 468 - Avg last five number = 35 ⇒ 35 × 5 = 175 - Avg first four number = 40 ⇒ 4 × 40 = 160 - Let 5th number = x - 6th number = x + 6 - 7th number = x – 5 - ⇒ 39 × 12 = 468 - ⇒ 35 × 5 = 175 - ⇒ 4 × 40 = 160 - 175 + 160 + x + x + 6 + x - 5 = 468 - 335 + 3x + 1 = 468 - 3x = 132 - x = 44 - (5th + 6th) / 2 = (x + x + 6) / 2 = (44 + 44 + 6) / 2 = 47