Question

What should be added to each of the numbers 13, 17 and 22 so that, the resulting numbers are in continued proportion?

Continued proportion means a:b : : b:c

• A. 4
• B. 5
• C. 6
• D. 3

Answer 1

The correct option is D

3

Three numbers 'a', 'b' and 'c' are said to be continued proportion if a, b and c are in proportion. Thus, if a, b and c are in continued proportion, then a, b, b, c are in proportion i.e. a : b : : b : c.

So, $\frac{a}{b}=\frac{b}{c}$

Let the required number to be added is x

$\therefore$ 13 + x, 17 + x and 22 + x are in continued proportion.

$\Rightarrow \frac{13+x}{17+x}=\frac{17+x}{22+x}$

$\Rightarrow (13+x)(22+x)=(17+x{)}^2$ [Cross multiplication]

$\Rightarrow 286+35x+x^2=289+34x+x^2$

$\Rightarrow 35x-34x=289-286$

$\Rightarrow x=3$

$\therefore$ The required number to be added is 3.