Average is the area where you can score maximum marks in minimum time. So study and practice maximum questions. Getting average marks in competitive exams do not help in achieving good job.
TYPE-I
*Average=Sum of all observations/ Number of observations *If the average of 'm' observations is 'x' and the average of'n' observations is V then the Average of the new group formed by combining the two groups is Average=mx ny/mn
EXAMPLES
1.
Find the average of all prime numbers between 30 and 50. Prime numbers between 30 and 50 = 31, 37, 41, 43 and 47 Average =sum/number =31 374143 47/5 =199/5=39.8
2.
The average weight of P, Q and R is 45 kg. If the weight of P and Q is 40kg and that of Q and R is 43kg, find the weight of Q. P Q R= 45 x 3 = 135kg P Q = 40 x 2 = 80 kg QR = 43 x 2 = 86 kg Q = (PQ) (Q R)-(P QR) =80 86 - 135 = 31kg
3.
The average of 11 numbers is 60. If the average of first 6 numbers is 58 and the average of last 6 numbers is 63, which is the 6th number. = (6 x 58) (6 x 63) - (11 x 60) = (348 378) - 660 = 726-660 = 66 .'.the 6th number = 66
4.
The average of two numbers is P. If one number is Q, then the other number is Let the other number be x so X Q/2 =P x Q =2P x =2P-Q .'.the other number is 2P - Q
5.
Find the product of the third and the fifth numbers, if the average of 5 consecutive odd numbers is 57. Given, average of x1, x3 x5, X7 and X9 is 57 So x5 =57 and x9 = 61 .'.Product = 57 x 61 = 3477
TYPE-II
*When a new item is added to a group of items, the average changes and the value of new item added is given by Value of new item = New average (difference in average x number of items before) *When an item is removed from a group of items the average changes and the value of removed item is given by. Value of removed item = Old average (difference in average x number of items new)
EXAMPLES
1.
The average age of 3 friends is 27 yrs. If the age of 4th friend is added, their average becomes 28 yrs. What is the age of the 4th friend. 3x 27 = 81 4x 28 = 112 .'.Age of 4th friend = 112- 81 = 31 yrs
2.
In a class of 22 students with an average weight of 45kg, one student of weight 50kg left. Instead another student came and the average weight became 46. The weight of the new student is Weight of new student = 50[22x (46-45)] = 50 22 = 72kg
3.
In a house, the average weight of 12 members and the grandmother is 17kg. If the weight of the grandmother is not included, the average decreases by 2kg. Find the weight of the grandmother Weight of grandmother = 15[13(17-15)] = 15 (13x2) = 15 26 = 41 kg .'.Weight of grandmother = 41kg
TYPE - III
*If one travelled from A to B at x km/hr and returned to A at y km/hr, then his average is given by. Average =2xy/xy *If one travelled from A to B at x km/hr and from B to C at y km/hr, then his average speed is given by Average=xy/2
EXAMPLES
1.
A car started from Kollam to Kottayam at a speed of 40 km/hr and returned back to Kollam at the speed of 60 km/hr. What is the average speed of the car. =2xy/xy 2x40x60/4060
2.
The average speed of a bus for the first 150 km is 50 km/hr, the next 50km is 25 km/hr and the last 30 km is 15 km/hr. Find the average speed of the bus for the entire journey. Total distance covered by the car = (150 50 30)km = 230km Total time of travel =[150/5050/2530/15]hr = (3 2 2)hr = 7 hr .'.Average speed = 230/ 7 = 32.85 km/hr
3.
Vinod travelled to office 180km away from his home at an average speed of 60 km/hr and returned home at 40 km/ hr. What is his average speed for the whole journey. =2xy/x y =2x60x40/6040 = 2x60x40/100 =4800/100 = 48 .'.Average speed = 48 km/hr.
POINTS TO REMEMBER
1.
Average of first 'n' natural numbers =(n1/2)
2.
Average of first 'n' even numbers =n1
3.
Average of first 'n' odd numbers =n
4.
Average of cons-ecutive numbers =First No. last No./2 =2x40x60/100= 48 .'.Average speed of the car = 48 km/hr
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