Ratio and Proportion — MATHS STD 7 — Question

1. 243

Solution:

Let the third proportional of 3 and 27 be x.

Then,

$3:27::27:\text{x}$

$\Rightarrow3:27=27:\text{x}$

$\Rightarrow\frac{3}{27}=\frac{27}{\text{x}}$

$\Rightarrow3\text{x}=27\times27$

$\Rightarrow\text{x}=\frac{27\times27}{3}$

$\Rightarrow\text{x}=27\times9$

$\therefore\text{x}=243$

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

Hence, the correct alternative is option (a).