Fast Track Techniques to solve the QUESTIONS of AVERAGE

1. If the average of n1 observations is a1, the average of n2 observations is a2 and so on, then
          average age of the all the observations
                           = ( n1 a1 +n2 a2+.........) /(n1 + n2 +........) 

Q. There are 30 boys and 60 girls in a class. If the average age of boys is 12 yr and average age of girls is 10 yr, then find out the average age of the whole class.
 EXPLANATION
      Here n1 = 30, n2 =60, a1 = 12, a2 = 10
Average age of the whole class = ( 30× 12 + 60× 10)/ (30+ 60)
                             = 960/90 = 10.66 yr
2. If the average of m observations is a and the average of n observations taken out of m is b, then
 average of rest of the observations = ( ma - nb) /(m - n)


Q. A man bought 20 cows in 200000. If the average cost of 12 cows is 12500, then what will be the average cost of remaining cows?
EXPLANATION
Average cost of 20 cows = 200000/20 = 10000
Here m = 20, n = 12, a = 10000, b = 12500
Average age of remaining (20 - 12)cows
                      = ( 20 × 10000 - 12× 12500) /( 20 - 12)
                      =  50000/8
                      =  6250

Fast Track Techniques to solve the  QUESTIONS of HCF & LCM

3. If average of n observations is a but the average becomes b when one observation is eliminated, then value of eliminated observation = n (a - b) + b

Q. In a cricket team, the average age of 11 players and the coach is 18 yr. If the age of the coach is not considered, then the average decreases by 1 yr. Find out the age of the coach.
EXPLANATION
Here,   n = 11+ 1= 12;
       Initial average (a) = 18 yr;
       Last average (6) = 18-1= 17yr
       Age of the coach = n (a - b) + b
                                      =12 (18 - 17) + 17
                                      = 12 + 17
                                      = 29yr

4. If average of n observations is a, but the average becomes b when a new observation is added, then Value of added observation =n(b - a) + b

Q. The average run scored by a batsman in 20 innings is 32. After 21st innings, the runs average becomes 34. How much runs does the batsman score in his 21st innings?
EXPLANATION
Here, n = 20;
       Initial average, a = 32;
       Last average, (6) = 34
   .'. Runs scored in 21st innings = n (b - a) + b
                                = 20 (34 - 32) + 34
                                = 20 x 2 + 34
                                = 74

5. If the average of total components in a group is a, where average of n components (1st part) is b and average of remaining components (2nd part) is c, then
    Number of remaining components (2nd part)
            = n ( a - b) /( c- a)

Q. The average salary of the entire staff in an office is 200 per day. The average salary of officers is 550 and that of non-officers is  120. If the number of officers is 16, then find the numbers of non-officers in the office.
EXPLANATION
Here n = 16, a = 200, b = 550, c = 120
Number of non-officers = n( a - b) / ( c - a)
                                           = 16 ( 200 - 550)/ ( 120 - 200)
                                           = 70