Question

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, what is the average marks of all the three classes put together

Answer 1

Given:

Average marks of class a = 30

Average marks of class b = 50

Average marks of class c = 70

Average marks of class a and b = 45

Average marks of class b and c = 65

Define variable:

Let the number of students in class a = x

Let the number of students in class b = y

Let the number of students in class c = z

Find each class total marks:

$\text{Total marks} = \text{Total students} \times \text{Average marks}$

$\text{Total marks for Class a} = 30x$

$\text{Total marks for Class b} = 50y$

$\text{Total marks for Class c} = 70z$

Find the average marks of class a and b:

$\text{Total students} = x + y$

$\text{Total marks} =30x + 50y$

$\text{Average marks} =\dfrac{30x + 50y}{x + y}$

Given that the average marks of class a and b is 45:

$\dfrac{30x + 50y}{x + y} = 45$

$30x + 50y = 45( x + y)$

$30x + 50y = 45 x + 45y$

$5y = 15x$

$y = 3x \text {------------------[ 1 ]}$

Find the average marks of class b and c:

$\text{Total students} = y + z$

$\text{Total marks} =50y + 70z$

$\text{Average marks} =\dfrac{50y + 70z}{y + z}$

Given that the average marks of class b and c is 65:

$\dfrac{50y + 70z}{y + z}} = 65$

$50y + 70z = 65( x + y)$

$50y + 70z = 65x + 65y$

$5z = 15y$

$z = 3y \text {------------------[ 2 ]}$

Substitute [ 1 ] into [ 2 ]:

$z = 3( 3x)$

$z = 9x$

Find the number of students in each class in term of x:

$\text{Class a} = x$

$\text{Class b} = y$

$\text{Class b} = 3x$

$\text{Class c} = z$

$\text{Class c} = 9x$

Find the average number of students of class a, b and c:

$\text{Total students} = x + 3x + 9x$

$\text{Total students} = 13x$

$\text{Total marks} = x(30) + 3x(50) + 9x(70)$

$\text{Total marks} = 30x + 150x + 630x$

$\text{Total marks} = 810x$

$\text{Average marks} = \dfrac{810x}{13x}$

$\text{Average marks} = 62.3 \text{ marks}$

Answer: The average marks of the 3 classes is 62.3 marks