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# Averages - competitive exams

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• 1. Averages Dr. S. Murali Professor &amp; Head Dept. of Mechanical Engineering 1
• 2. Definition &#x2022; The average of any set of quantities can be found by adding all the numbers together then dividing by the number of quantities in the set &#x2022; average = total of quantities / number of quantities 2
• 3. Math Formula Formula Sum of Observations Number of Observations 3
• 4. Initial Avg. Final Avg. In a Crude way- Simple Final Avg. =Initial + Diff. 4
• 5. In a Crude way- Simple Excess Final Avg. Deficiency Excess loss = Deficiency gain 5
• 6. 1. Find the average of 4,6,9 and 11 Sol: given numbers are small apply conventional formula Sum of the numbers is = 30 Average = Sum/No. of Numbers =30/4 =7.5 6
• 7. 2. Find the average of 146,152, 149, 157 and 162 Sol: Numbers are larger: avoid using conventional method Method 1 146 152 149 162 157 assume average 146 and excess available at other numbers are Sum 0 +6 +3 +16 11 36 This excess is shared among 6 numbers =36/5=7.2 Average of 6numbers is =Assumed avg. + avg. of excess 146+7.2=153.2 7
• 8. 146,152, 149, 157 and 162 Method 2 arranging the numbers in ascending order 146 149 152 157 162 assume average 152 and find excess/less available at other numbers are -6 -3 0 5 10 Sum This excess is shared among 6 numbers =6/5=1.2 6 Average of 5 numbers is =Assumed avg. + avg. of excess 152+1.2=153.2 8
• 9. 3. Find the average of 16,24,32,40 and 48 Sol: 8 16 8 8 24 32 8 40 48 Series in Arithmetic Progression with odd numbers(5) Hence middle number 32 is the average 9
• 10. 4. Find the average of 16,24,32,40,48 and 56 Sol: 8 16 8 8 24 32 8 40 8 48 56 Series in Arithmetic Progression with even numbers(6) Average of middle numbers is the average =(32+40)/2=36 10
• 11. 5.The avg. of 7 consecutive numbers is 33. the largest of these numbers is? Sol: 7 consecutive numbers X-3 X-2 X-1 X X+1 X+2 X+3 X X+2 X+4 X+6 X X+1 X+3 X+5 7 consecutive even numbers X-6 X-4 X-2 7 consecutive odd numbers X-5 X-3 X-1 All these combinations are in AP and as 7 being odd number, the middle number equals to the average The largest of numbers is x=33+3=36 11
• 12. 6. The avg. of 30 students in a class is 12 years. The avg. age of a group of 5 of the students is 10 years and that of another group of 5 of them is 14 years. What is the avg. of the remaining students? 10 14 10 12 20 10 5 5 Excess of 5 students =less required by 5 students No change in remaining average, hence average of remaining is 12 12
• 13. 7. The average of eight numbers is 14. the average of six of these numbers is 16.What is the average of remaining two numbers. 16 14 8 Gain by 6 = loss by 2 12 = x 2 Average loss=6 Average of remaining two = 14-6=8 13
• 14. 8. If the average mark of a student in four examinations is 40. If he got 80 marks in 5th Examination. What is the New average ? Sol: 40 80-40=40 80 Assume Avg. of 5 books is 40 Excess available at 5th book is 40 Increase in average =40/5=8 New average =40+8 =48 14
• 15. 9. If the average mark of a student in four examinations is 40. If he got 20 marks in 5th Examination. What is the New average ? Sol: 40 20-40=-20 20 Assume Avg. of 5 books is 40 less shared by 5th book is 20 Decrease in average =-20/5=-4 New average =40-4 =36 15
• 16. 10. If the avg. age of 30 boys in a class is 15 yrs. When the age of class teacher is included the avg. is 16 years. What is the age of the class teacher? Sol: 16 X 15 15 Un contributed age of teacher =Avg. of students= 15 Avg increase due to teacher addition is =New avg &#x2013; initial avg = 16-15=1 Distributed age of teacher =X=1&#xD7;31=31 Teacher age=assumed average + surplus =15+X=15+31=46 16
• 17. 11. The average of 50 numbers is 38. What is the average of the numbers, if two numbers namely 45 and 55 are discarded. Excess at 45 and 55 is =7+17=24 55 38 45 7 17 Less available at 48 numbers is =24/48=0.5 The average of 48 numbers is =38-0.5 =37.5 17
• 18. 12. In a group the Avg. income of 6 men is Rs. 500 And that of 5 women is Rs. 280. What is the average income of the group? Sol: Assume average of 11 members as 280 500-280=220 280 Then excess average available with 6 men=500-280=220 Total excess income available with 6 men=6&#xD7;220 500 280 6 5 Increase in average of 11 members =6&#xD7;220/11=120 New average =280+ 120=400 18
• 19. 13. A class has 2 sections, in one of which there are 40 students with an average of 14.5 years. The average of the class is 14.2 years . If there are be 32 students in the other section, its average is ? 14.5 Excess available at 40 students =0.3 &#xD7; 40=12 Increase in average 32 students =12/32=0.375 Average of 32 students x = 14.2-0.375 x = 13.825 14.2 0.375 x 40 32 19
• 20. 14. The average of 11 observations is 60. if the average of first five observations is 58 and that of last five is 56, then the sixth observations is Excess 60 /11 56 /5 Excess supplied by sixth observation to first five and last five is = 4*5+2*5 =30 Sixth observation=60 + 30=90 20
• 21. 15. Mukhesh has twice money as sohan and sohan has 50% more money than pankaj has. If the average money of with them is Rs. 110, then muksh has 3x 1.5x Total money available 110 x =110*3 3x+1.5X+x =110*3 5.5 x = 110 *3 x = 110/5.5*3 x =60 Mukhesh money= 1.5 x 60=90. 21
• 22. 16. Three years ago, the average age of a family of 5 members is 17 years. A baby having been born. the average age of the family is the same today. What is the present age of the baby 20 Excess 17 15 2 Excess supplied 5 family members to the baby is = 3*5 =15 Age of the baby is=17 - 15=2 22
• 23. Our head weights have been Averaged ? Thank you Contact smuralichinna@gmail.com 23
• 24. Puzzle 1. A series from 1-9 is arranged in the boxes as shown such that the sum along vertical and horizontal direction is 13. find the number at G block? Sol: 1 2 34 5 67 8 9 A B C D E F G H I 24
• 25. Thank you for patience Contact smuralichinna@gmail.com 25