Question

there are four unknown numbers, the mean of first two numbers is 4 and mean of first three numbers is 9 the mean of all four numbers is 15 if one of the number is 2 find other numvers

Answer 1

Let numbers be x1,x2,x3 and x4
We have x1 = 2

We are given,

x1 + x2 = 8
so, x2 = 8-2 = 6 

Then, x1 + x2 + x3 = 27
       so, x3 = 27 -8
             x3 = 19

We also have, x1+x2 + x3 + x4 = 60
          so, 27 + x4 = 60 
            so, x4 = 33

Hence, Numbers are 2,6,19 and 33 
   

Answer 2

Answer:

The four numbers are 2, 6, 19, 33

Step-by-step explanation:

Let the number be $x_{1},x_{2},x_{3},x_{4}$

According to the question

The mean of first  two numbers = 4

and one of the number is 2.

So, suppose $x_{1} = 2$

We know that

$mean = \frac{sum\ of\ the\ observation}{total\ no.\ of\ observation}$

$4 = \frac{x_{1}\ +\ x_{2}}{2}$

$4 = \frac{2\ +\ x_{2}  }{2}$       ∵ $x_{1} = 2$

$8 = 2\ +\ x_{2}$

$8\ -\ 2 = x_{2}$

$x_{2} = 6$

And the mean of first three numbers = 9

So,

$9 = \frac{2\ +\ 6\ +\ x_{3}}{3}$

$27\ -\ 8 = x_{3}$

$x_{3} = 19$

Now, the mean of all four numbers = 15

$15 = \frac{2\ +\ 6\ +\ 19\ +\ x_{4} }{4}$

$60 = 27\ +\ x_{4}$

$60\ -\ 27 = x_{4}$

$x_{4} = 33$

Hence the four numbers are 2, 6, 19, 33.