Question

The average marks of 15 students of a class
was increased by 3 when three of them with
marks 70, 20 and 60 were replaced by X, Y&Z.
Find the average of X, Y & Z.​

Answer 1

Given :

The number of students in class = 15

The marks of three students = 70 , 20 , 60

The average  marks of 15 students increase by 3 , when new students replace is X , Y , Z

To Find :

The average marks of students X , Y , Z

Solution :

Let The average of 15 students = A

Or,       $\dfrac{x_1+x_2+x_3+..........+x_1_5}{15}$   = A

Or, $\dfrac{x_1+x_2+x_3+..........+x_1_2+70+20+60}{15}$ = A

Or, $x_1+x_2+x_3............+x_1_2$ + 150 = 15 A

∴  , $x_1+x_2+x_3............+x_1_2$ = 15 A - 150

Now,

The Average is increase by 3 when X, Y , Z replace students marks 70 , 20 , 60

Or, $\dfrac{x_1+x_2+x_3+..........+x_1_2+X+Y+Z}{15}$ = A + 3

Or, , $x_1+x_2+x_3............+x_1_2$ + X + Y + Z = 15 ( A + 3 )

Or, 15 A - 150  + X + Y + Z = 15 ( A + 3 )

Or,  X + Y + Z = 15 ( A + 3 ) - ( 15 A - 150 )

Or,  X + Y + Z = 15 A + 45 - 15 A + 150

Or,  X + Y + Z = 195

Again

The average of X , Y , Z = $\dfrac{X+Y+Z}{3}$

                                       = $\dfrac{195}{3}$

                                       = 65

Hence, The The average marks of X , Y , Z students is 65  . Answer