Question

What number must be added to each of the numbers $25,35,40,55,$ so that new numbers are in proportion?

Answer 1

Given: $25,34,40,55$

Now, let $x$ be the number that must be added, so that the given numbers are in proportion.

$\Rightarrow 25+x:35+x::40+x:55+x$

$\Rightarrow \frac{25+x}{35+x}=\frac{40+x}{55+x}$

$\Rightarrow (25+x)(55+x)=(40+x)(35+x)$

$\Rightarrow 1375+25x+55x+x^2=1400+35x+40x+x^2$

$\Rightarrow 1375+80x=1400+75x$

$\Rightarrow 80x-75x=1400-1375$

$\Rightarrow 5x=25$

$\Rightarrow x=5$

Hence, the number that should be added so that $25,34,40,55$ are in proportion is $5$.