Question # 2
The average marks of three classes, A, B, and C are 30, 50, and 70, respectively. If the average marks of classes A
and B together is 45, and that of classes B and C together is 65, then what is the average marks of all the three
classes put together?
Answers
Step-by-step explanation:
Given :-
The average marks of three classes, A, B, and C are 30, 50, and 70, respectively. If the average marks of classes A and B together is 45, and that of classes B and C together is 65.
To find :-
What is the average marks of all the three
classes put together?
Solution :-
Given that
Average marks of the class A = 30
Let the students in the class A be a
We know that
Average = Sum of all observations/Number of all observations
Total marks of the class A = 30a
Average marks of the class B = 50
Let the students in the class B be b
Total marks of the class B = 50b
Average marks of the class C = 70
Let the students in the class C be c
Total marks of the class C = 70c
Given that
Average of marks of classes A and B = 45
We know that
Average = Sum of all observations/Number of all observations
Average marks of classes A and B = Sum of the marks of the classes A and B / Number of students
=> 45 = (30a+50b)/(a+b)
=>45(a+b) = 30a+50b
=> 45a +45b = 30a +30b
=> 45a +45b -30a -50b = 0
=> (45a-30a)+(45b-50b) = 0
=> 15a -5 b = 0
=> 15a = 5b
=> b = 15a/5
=> b = 3a ---------------(1)
Average of marks of classes B and C = 65
We know that
Average = Sum of all observations/Number of all observations
=>65=(50b+70c)/(b+c)
=>65(b+c) = 50b+70c
=> 65b + 65c = 50b +70c
=> 65b+65c -50b -70c = 0
=> (65b-50b) +(65c-70c) = 0
=> 15b -5c = 0
=> 5c = 15b
=> c = 15b/5
=> c = 3b -------------(2)
On Substituting the value of b in (2) from (1)
=> c = 3(3a)
=> c = 9a -----------(3)
Number of students in A = a
Number of students in B = 3a
Number of students in C = 9a
Total number of students in all the three classes A ,B and C
=> a + 3a + 9a
=> 13 a
Total marks of all the classes of A ,B and C
= 30a + 50b + 70c
=> 30a + 50(3a) +70(9a)
=> 30a + 150a +630a
=> 810a
Average = Sum of all observations/Number of all observations
Average of the marks of the all classes
=> 810a/13a
=> 810/13
=> 62.307...
=> 62.3 (correct it one decimal )
Answer:-
The average marks of all the classes A ,B and C is 62.3
Used formulae:-
Average = Sum of all observations/Number of all observations