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 number is $15$, if one of the four number is $2$ find the other numbers

Answer 1

Let $A,B,C,D$ be the numbers.

Given, $\frac{A+B}{2}=4$ $⟹A+B=8$ ------(i)

Given, $\frac{A+B+C}{3}=9$ $⟹A+B+C=27$ ------(ii)

$8+C=27$ -----from(i)

$C=27-8=19$

Given, $\frac{A+B+C+D}{4}=15$ $⟹A+B+C+D=60$ ------(iii)

$27+D=60$ ------from(ii)

$D=60-27=33$

Given, one of the numbers, among $A,B,C,D$ is $2$. Let $A=2$.

From (i), $A+B=8$

$⟹B=6$

Hence the numbers are $2,6,19,33$