Question

Mark the correct alternative in the following question:

The third proportional of 3 and 27 is

(a) 243 (b) 256 (c) 289 (d) 225

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{third}\mathrm{proportional}\mathrm{of}3\mathrm{and}27\mathrm{be}x.\mathrm{Then}, \\ 3:27::27:x \\ \Rightarrow 3:27=27:x \\ \Rightarrow \frac{3}{27}=\frac{27}{x} \\ \Rightarrow 3x=27\times 27 \\ \Rightarrow x=\frac{27\times 27}{3} \\ \Rightarrow x=27\times 9 \\ \therefore x=243 \end{gathered}$$

So, the third proportional of 3 and 27 is 243.

Hence, the correct alternative is option (a).