Question

There are four unknown numbers. The mean of the first two numbers is 4 and the mean of the first three is 9. The mean of all four numbers is 15. If first of the four numbers is 2, find the other 3 numbers.

Answer 1

Let the 4 numbers be a , b , c and d
Mean of the first 2 numbers, a and b = 4
So, a + b = 4 $\times$ 2 = 8 — (i)
Mean of the first 3 numbers, a, b and c = 9
So, a + b + c = 9 $\times$ 3 = 27 – (ii)
From equations (i) and (ii),
Third number, c = 27 - 8 = 19
Mean of all the 4 numbers = 15
So, a + b + c + d = 15 $\times$ 4 = 60 – (iii)
From equations (ii) and (iii),
Fourth number,d = 60 - 27 = 33
Now, we got 2 unknown numbers; c = 19 and d = 33
It is given in the question that one of the numbers is 2
So, let a = 2
Therefore, the third unknown number, b = 60 - ( 19 + 33 + 2)
$\Rightarrow$ b = 6
Hence, the three other numbers are 6, 19 and 33.