Question

If a < b < 2a and mean and median of a, b and 2a are 15 and 12 respectively, then a = _________.

Answer 1

The given observations are a, b and 2a.

Mean of the given observations = 15
$$\begin{gathered} \therefore \frac{a+b+2a}{3}=15 \\ \Rightarrow 3a+b=45.....\left(1\right) \end{gathered}$$

If the number of observations i.e. n is odd, then

Median = $\left(\frac{n+1}{2}\right)\mathrm{th}$ observation

Here, n = 3.

Median of the given observations = 2nd observation = b = 12 .....(2)

From (1) and (2), we get

$$\begin{gathered} 3a+12=45 \\ \Rightarrow 3a=45-12=33 \\ \Rightarrow a=11 \end{gathered}$$

If a < b < 2a and mean and median of a, b and 2a are 15 and 12 respectively, then a = ____11____.