In a survey $243$ people were asked if they preferred butter, margarine or cheese. The ratio of people who preferred cheese to margarine was $7:2$. Two thirds of the whole sample preferred butter. How many people preferred cheese?

Total number of people = 243

Number of people, who preferred butter 

$$\begin{gathered} =243\times \frac{2}{3} \\ =162 \end{gathered}$$

Number of people, who preferred either cheese or margarine 

$=243-162=81$

Let, the number of people who preferred cheese and margarine is $7\mathrm{x}$ and $2\mathrm{x}$respectively.

$\begin{array}{l}\therefore 7x+2x=81\\ \Rightarrow 9x=81\\ \Rightarrow x=9\end{array}$

So, Number of people, who preferred cheese

$=7x=7\times 9=63$