Question

What number shall be added to each of the numbers $4,7,14,22$ to form the terms in a proportion?

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

Let the number to be added be ' $x$'
$\therefore$ $(4+x),(7+x),(14+x),(22+x)$ are in proportion.
$\Rightarrow$ $(4+x)(22+x)=(7+x)(14+x)$
$\Rightarrow$ $88+4x+22x+x^2$ $=98+7x+14x+$ $x^2$
$\Rightarrow$ $88+26x=98+21x$
$\Rightarrow$ $26x-21x=98-88$ $\Rightarrow$ $5x=10$
$\Rightarrow x=\frac{10}{5}\Rightarrow x=2$