08 Average Exercise

Exercise 1. 2. 3. 4. 5. 6. Find the Average of first 13 odd no. (a) 13 (b) 11 (c) 12 (d) 9 Find the Average of square of first 17 natural no. (a) 105 (b) 110 (c) 115 (d) 100 The Average of 9 observations is 87. If the Average of first five observations is 79 and the Average of next three is 92. Find the 9th observation. (a) 111 (b) 112 (c) 110 (d) 113 The Average of 7 data is 34 and the Average of first 3 data is 28 and the Average of next two data is 47. Find the average of last 2 data. (a) 15 (b) 20 (c) 25 (d) 30 The average of 9 data is 79. The average of first two data is 75. and the average of next four data is 87. If the 8th data is 5 more than 7th data and 1 more than 9th data. Calculate 9th observation. (a) 69 (b) 70 (c) 72 (d) 71 The Avarage of 8 number is 20. The avg. of first two number is 15.5 and the avg. of next 3 (a) 10 (b) 31/3 (c) 34/3 (d) 32/3 8. 9 Girls and 1 Boy go to a restaurant for lunch. If each girl spent ` 30 and boy spent ` 72000 more than the average of expenditures of all. Find the amount spent by the boy. (a) ` 80000 (b) ` 85000 (c) ` 80030 (d) ` 90000 9. 3 years ago the average of family of five members was 17 years. A baby having been born the average age of the family is the same today. Find the age of the baby now. (a) 1 (b) 2 (c) 3 (d) 4 10. The average age of mother, father and son was 42 years at the time of the marriage of the son. After 1 year an infant was born and after 6 years of marriage the average age of the family becomes 36 years. Find the age of the bride at the time of the marriage. (a) 25 (b) 20 (c) 30 (d) 20 11. The average temp. of Monday, Tuesday, Wednesday and Thursday is 31ºc and the average temp of Tuesday, Wednesday, Thursday and Friday is 29.5ºc. If the average of 1 . If the 6th no. 3 is 4 less than the 7th and 7 less then the 8th number Find the 8th number ? (a) 25 (b) 30 (c) 35 (d) 20 The average age of 30 students of a class is 14 years 4 months. Due to admission of 5 new students the average becomes 13 years 9 months, while the age of the younger one among new 5 students is 9 years 11 months. Find the average of remaining four new students. 1 % 2 more than the average temp of Friday. Find the temp. of Monday. (a) 21º C (b) 20º C (c) 22º C (d) 23º C 12. The average temp from Monday to Wednesday is 37ºC while the average temp from Tuesday to Thursday is 34ºC. The temp of Thursday is 4/5 times to that on Monday. Find the temp on Thursday. (a) 31º C (b) 36º C number is 21 7. Average temp on Monday was 37 110 (c) 30º C (d) 35º C 13. There were 42 students in a Hostel due to admission of 13 new students expense of mess is increased by Rs. 30 per day while per day expenditure per student is reduced by Rs. 3. What was the original expenditure of mess per day. (a) 600 (b) 610 (c) 630 (d) 620 14. There are 4 natural no. if average of any 3 no. is added with 4th no. 29, 23, 21 and 17 will be obtain find all 4 natural no.? (a) 18, 21, 6, 3 (b) 21, 15, 12, 6 (c) 18, 15, 12, 9 (d) 21, 12, 9, 3 15. There are 3 natural no. if average of any 2 no. is added to the third no. 24, 20 and 18 will be obtained. Find all the natural no. (a) 6, 8, 17 (b) 9, 6, 16 (c) 9, 5, 17 (d) 12, 6, 13 16. The average age of boys of a school is 12 years and of girls is 11 years. If the total no. of boys is 480. Then find the no. of girls if the average age of school 11 years 9 months. (a) 160 (b) 150 (c) 140 (d) 170 17. I f the bowling average of a bowler is 12.4 run per wicket. He takes 10 wickets in his next innings by giving 52 runs, due to this his bowling average is improved by 0.4 run per wicket. Find the total no. of wickets taken by him at present. (a) 150 (b) 160 (c) 180 (d) 170 18. A batsman scores 87 runs in his 17th innings due to this his average increased by 3 runs. Find his current average. (a) 35 (b) 40 (c) 36 (d) 39 19. The bowling average of a bowler in certain matches is 12.4 runs per wicket. If he takes 5 wickets for 26 runs in his next innings then his bowling average becomes 12 runs per wicket. Find the wickets taken by him in the last inning. (a) 90 (b) 85 (c) 80 (d) 95 20. The average weight of some students in a class is 43 kg. When 4 new students are included the average weight becomes 42.5 kg and the weight of those 4 students are 42, 36.5, 39 and 42.5 kg. Find the total no. of students in the class. (a) 20 (b) 24 (c) 22 (d) 30 21. A batsman has an average of 30 runs in his 42 innings. The difference between his max. and min. score is 100. If these 2 innings are removed his average for 40 innings comes down to 28. What is his max. score? (a) 120 (b) 110 (c) 125 (d) 130 22. The average of six innings of a player is 3.95. The average of two innings is 3.4 while the average of next two innings is 3.85. What is the average of last two innings: (a) 4.5 (b) 4.6 (c) 4.9 (d) 4.8 23. A batsman in his 16th innings makes a score of 60 and there by increase his average by 3. What is his average after 16 th innings ? (a) 18 (b) 20 (c) 15 (d) 21 24. The average of five consecutive natural number is m. If the next three natural numbers are also included, how much more than m will the average of these numbers be? (a) 1 (b) 1.5 (c) 1.4 (d) 2 25. The average of four positive integers is 72.5. The highest in- teger is 117 and the lowest integer is 15. The difference between the remaining two integers is 12. Which is the higher of these two remaining integer ? (a) 70 34. (b) 73 (c) 85 (d) Can’t be determined 26. The average of nine consecutive odd numbers is 53. The least odd number is : (a) 22 (b) 27 (c) 35 (d) 45 27. The average of all odd numbers less than 100 is : (a) 49.5 (b) 50 (c) 50.5 (d) 51 28. The average of seven consecutive positive integers is 26. The smallest of these integers is: (a) 21 29. 30. 31. 32. 33. (b) 23 (c) 25 (d) 26 Total weekly emoluments of the worker s of a factory is Rs.1534. A verage weekly emolument of a worker is Rs. 118. The number of workers in the factory is : (a) 16 (b) 14 (c) 13 (d) 12 The average of 10 numbers, a student, by mistake, wrote 64 in place of a number 46 and got his correct average 50. The correct average of the given numbers is: (a) 48.2 (b) 48.3 (c) 49.1 (d) 49.3 If the average of 20 observations x1, x2.....x20 is y, then the average of x 1–101, x 2–101, x2 – 101........x20–101 is : (a) y - 20 (b) y -101 (c) 20y (d) 101y The average of 27 numbers is 60. If one number is changed from 28 to 82, the average is : (a) 56 (b) 58 (c) 62 (d) 64 The mean value of 20 observa- 111 35. 36. 37. 38. 39. tions was found to be 75, but later on it was detected that 97 was misread as 79. Find the correct mean. (a) 75.7 (b) 75.8 (c) 75.9 (d) 75.6 The average of 7 consecutive numbers is 20. The largest of these numbers is : (a) 24 (b) 23 (c) 22 (d) 20 Eight consecutive numbers are given. If the average of the two numbers that appear in the middle is 6, then the sum of the eight given numbers is: (a) 54 (b) 64 (c) 36 (d) 48 The average of seven numbers is 18. If one of the numbers is 17 and if it is replaced by 31, then the average becomes : (a) 21.5 (b) 19.5 (c) 20 (d) 21 If the mean of 4 observations is 20, when a constant ‘C’ is added to each observation, the mean becomes 22. The value of C is: (a) 6 (b) -2 (c) 2 (d) 4 The mean of 11 numbers is 35. If the mean of first 6 numbers is 32 and that of the last 6 numbers is 37, find the sixth number : (a) 28 (b) 29 (c) 30 (d) 27 The average weight of the 8 oarsmen in boat is increased 1 2 by 1 kg when one of the crew who weighs 60 kg is replaced by a new man. The weight of the new man in kg is : (a) 70 (b) 68 (c) 71 (d) 72 40. Average of first five odd multiples of 3 is : (a) 12 (b) 16 (c) 15 (d) 21 41. If the average of x numbers is y 2 and that of y number is x 2 then tha average (x + y) number is: Average x (a) y (b) x - y (c) xy (d) x  y 42. If a,b,c,d,e,f,g are seven consecutive even integers, then what is their average ? (a) abcdefg 7 (b) 7(a + b + c + d + e + f + g) (c) a + 6 (d) a + 4 43. A car owner buys petrol at Rs.60, Rs.80, Rs.48 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs.12000 each year? (a) Rs.50 (b) Rs. 60 (c) Rs. 75 (d) Rs.80 44. The batting average for 40 innings of a cricket player is 40 runs. His highest score exceed his lowest by 56. If these two innings are excluded, the average of remaining 38 innings Average is 38 runs. The highest score of the player is (in runs): (a) 106 (b) 50 (c) 104 (d) 52 45. A cricketer has a certain average for 10 innings. In the eleventh innings, he scored 158 runs, thereby increasing his average by 10 runs. His new average is : (a) 58 (b) 68 (c) 48 (d) 78 46. A batsman has a certain average in 11 innings. In the 12th innings, he scored 90 runs and his average decrease by 5. After the 12 th innings what his average? (a) 150 (b) 145 (c) 155 (d) 140 47. A man buys a certain number of oranges at 20 for Rs.60 and an equal number at 30 for Rs.60. Find average rate of a orange? (a) Rs. 2.5 (b) Rs. 2.4 (c) Rs. 2 (d) Rs. 3 112 48. The average monthly salary of the workers in a workshop is Rs.8,500. If the a verage monthly salary of 7 technicians is Rs. 10,000 and average monthly salary of the rest is Rs. 7,800, the total number of workers in the workshop is: (a) 18 (b) 20 (c) 22 (d) 24 49. A lady bought 13 tops of Rs.50 each, 15 pants of Rs 60 each, 12 pairs of shoes at Rs.65 a pair and 20 pairs of socks at Rs.16 a pair. Find the average value of a article : (a) Rs.52 (b) Rs.44 1 6 (c) Rs.54 (d) Rs.55 50. If constant distance from home to school is covered by a boy at 10km/hr. The boy comes back the same distance at 15km/hr. Find his average speed during the whole journey (a) 12.5km/hr (b) 12km/hr (c) 10km/hr (d) 13km/hr Solution 1. (a) S = n2 = 132 average = n = 13 2. (a) sum = Average = = 3. n (n +1)(2n +1) 6n 6 18 ´ 35 = 105 6 (d) Last two data = (7 × 34) – (3 × 28 + 2 × 47) = 238 –178 = 60 35 ´ 55 11 496 – 430 – 9 = 4 12 12 \ average = = 1 124 = 10 3 12 8. (c) Sum (7th, 8th, 9th) = (9 × 79) – (2 × 75 + 4 × 87) = 711 – 498 = 213 7th + 8th + 9th = 213 (x –4) + (x + 1) + (x) = 213 Þ 3x – 3 = 213 (a) Let 6th number = x 7th number = x + 4 8th number = x + 7 (6th + 7th + 8th) = 160 – (31 + 64) x + x + 4 + x + 7 = 65 x = 18 30 30 30 30 (b) Sum = 30 × 14 4 or 30 × 12 1 43 14 = 30 × = 430 3 3 35 ´ 55 3 = 4 4 Sum (excluding four) New sum = 35 × 13 æ 11 ö ÷ = çç 430 + 9 12 ÷ è ø + [Boy] A + 72000 9 A + 8000 \ Boy = 8000 + 30 + 72,000 = Rs. 80,030 9. __ __ __ __ __ (b) 20 13. (c) Orig inal = 42x New = 55(x – 3) 42x + 30 = 55x – 165 13x = 195 Þ x = 15 \ original = 42×15= 630 14. (d) Let nos. be a, b, c and d. a +b +c + d = 29 3 (a + b + c + a) + 2d = 29 × 3 (29 + 23 + 21 + 17 – 90) a+b+c+d= 15 age of child = 17 – 15 = 2 years 10. (a) M F S Bride 48 average = Baby = 36 18 36 = 18 2 Bride + baby = 36 31y + 5y At time of marriage, bride = 31 – 6 = 25 years 11. (c) M + T + W + Th = 31 × 4 –(T + W + Th + F) = 29.5 × 4 M–F=6 37 1 3 %= 2 8 90 = 45 2 \ 45 + 2d = 87 d = 21 \ other number = 23 ´ 3 – 45 = 12 2 Other = 21´ 3 – 45 = 9 and 2 Other = 17 ´ 3 – 45 =3 2 5 × 3 17 \ 8th = x + 7 = 25 7. 496 12 ´ 4 (c) [1, 2, ........9] 60 average = = 30 2 x = 72 6. = (b) 9th observation = (9 × 87) – (5 × 79 + 3 × 92) = 783 – (395 + 276) \ 5. Sum (remaining 4) (n +1)(2n +1) = 783 – 671 = 112 4. \ 15. (c) a +b + c = 24 2 Þ a + b + 2c = 24 × 2 b +c + a = 20 Þ 2a + b + c = 20 × 2 2 a +c +b = 18 Þ a + c + 2b = 18 × 2 2 4(a + b + c) = 62 × 2 a + b + c = 31 \ c = 17, a = 9, b = 5 3 16. (a) 480 × 12 + x × 11 = 11 , 4 or \ M : F = 11 : 8 \ M = 22°C,F = 16°C 12. (b) M + T + W = 37 × 3 T + W + Th = 34 × 3 – – – – M – Th = 9 Th 4 36 = = M 5 45 B 12 G 11 113 4 3 4 1 4 =3:1 = 36ºC 113 Average nings = x – 3 1 = 160 \ girls = 480 × 3 16x = 15 (x – 3) + 60 x = 15 12.4x + 52 17. (c) = (12.0) x +10 n  (n  1)  (n  2)  (n  3)  (n  4) m 5 x = 170 n+2 = m wickets at present = 180 16x + 87 = 17(x + 3) 16x + 87 = 17x + 51  x = 36 \ New average = 36 + 3 = 39 19. (a) Runs = 12.4x 12.4x + 26 = 12 x +5 12.4x + 26 = 12x + 60 0.4x = 34 x = 85 Current wickets = 85 + 5 = 90 43x + 160 = 42.5x + 170 Þ 0.5x = 10 Þ x = 20 therefore, number of students = 24 21. (a) 30 × 42 = 1260 28 × 40 = 1120 20 tory  140 + 100 2 = 120 22. (b) The average of last 2 Innings. 3.95  6   3.4  2   3.85  2 2  4.6 23. (c) Let the averages of 16th innings = x Let the average after 15th inAverage 27. (b) Total no. of odd no. from 1 to 100= 50 Required average = 50 28. (b) x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 = 26  7  7x = 182 – 21 = 161 161  23 7 29. (c) Total no. of workers in fac- highest – lowest = 100  = m +1.5 Which is 1.5 more than m 25. (c) x + (x – 12) + 117 + 15 = 72.5  4 2x = 290 –117–15 + 12 = 170 x = 85 26. (d) x + x + 2 + x + 4 + x + 6 + x + 8 + x + 10 + x +12 + x + 14 + x + 16 = 9 × 53  9x + 72 = 477 x  highest + lowest = 140 Highest score = 8 405 x  45 9 = 42.5 120  m–2   m–1       m  4   m  5  9x = 477 – 72 = 405 43x + 42 + 36.5 + 39 + 42.5 20. (b) (x + 4) \ Þ n = m-2 Series is m–2, m–1, m, m+1, m+2, m+3, m+4, m+5 Average 18. (d) Let average be x \  60  24. (b) 12.4x + 52 = 12x + 120 = 82 – 28 = 54 Required average 1534  13 118 30. (a) Correct total number 10 numbers 50 × 10 – 64 + 48 = 482 482 average = = 48.2 10 33. (c) difference = 97 – 79 = 18 original average  75  32. (c) Difference of numbers 114 18 20 = 75.9 34. (b) Let 7 consecutive numbers is: x + x +1 + x + 2 + x +3 + x + 4 + x + 5 + x + 6 = 20 × 7 7x + 21 = 140 x = 17, largest numbers x + 6 = 117 + 6 = 23 35. (d) Let's the 1st no is x x + 3 + x + 4 = 2  6  2x + 7 = 12 5 2  x + (x + 1)+..........+(x + 7) = 8x + 28  2x  5  x   8 5  28  20  28  48 2 36. (c) Difference = 31 – 17 = 14  Required average 14  20 7 37. (c) 4C = 22  4 – 20  4 = 88 – 80 = 8 = 18  C= 8 =2 4 no. is= 6  32 + 6  37– 38. (b) 6th 11  35 = 192 + 222 – 385 = 29 39. (d) weight of new man = 60 + 8 ´ 3 2 = 60 + 12 = 72 kg 40. (c) Average of first five odd multiples of 3 31. (b) Required average x + x + ..... x 20 101´ 20 = y - 101 = 1 2 3 20 54  62 27 Þ 3(1 + 3 + 5 + 7 + 9) 3 ´ 25 = = 15 5 5 41. (c) sum = average × total observations Sx = y2  x = xy2 Sy = x2  y = x2y Sx + Sy = xy2 + x2y = xy(x + y) xy ( x + y ) Avergae = = xy x +y 42. (c) a = x, b = x + 2, c = x + 4, d = x + 6, e = x + 8, f = x + 10, g = x + 12 Average = x + x + 2 + x + 4 + x + 6 + x + 8 + x +10 + x +12 7 =x+6 i.e. =a+6 43. (b) uses of petrol in 1st year  12000  2 0 0 litre. 60 uses of petrol in 2nd year 12000  150 litre 80 uses of petrol in 3rd year 12000  250 litre 48 average cost  12000  3  Rs.60 200  150  250 44. (a) 40 × 40 – 38 × 38 = 1600 – 1444 = 156 Sum of these 2 innings = 156 i.e. x + x + 56 = 156 2x = 100 x = 50 Highest score = 50 + 56 = 106 45. (a) Let the average of 10th innings = x, then  10x  158  x  10 11 10x  158  11x  110 , x  48 New average = 48 + 10 = 58 46. (b) Let the average in 11th innings = x 145 47. (a) 20 orange of = 60 then 60 orange of = 180 30 orange of = 60 then, 60 orange of = 120 Average 180120 300   Rs.2.5 6060 120 = 48. (c) Let the workers in the workshop = x Then, 8500×x = 1000  7 + 7800(x-7) 8500 × x – 7800 × x = 1000 × 7 – 7800 × 7 700x = 2200  7 x = 22 49. (b) Average cost = 13 ´ 50 + 15´ 60+12´ 65+20´ 16 13+15+12+20 The average of after 12th match = =x-5 12(x – 5) = 11x + 90 x = 150 Hence, New average = 150-5 = 1 = Rs.44 6 50. (b) Average speed  115 650 + 900 + 780 + 320 60 2 10 15 12 km/hr 10 15 Average