Tag: ratio, proportion and unitary method

Given a : b = 8 : 9, b : c = 18 : 40
$\displaystyle {\frac{a}{c}\, =\, \frac{a}{c}\, \times\, \frac{b}{b}\, =\, \frac{a}{b}\, \times\, \frac{b}{c}\, =\, \frac{8}{9}\, \times\, \frac{18}{40}\, =\, \frac{2}{5}}$
a : c = 2 : 5

Let the third number be x.
Then first number=120% of x=$\frac{120}{100}\times x=\frac{6x}{5}$
Second number=150% of x$\frac{150}{100}\times x=\frac{3x}{2}$
$\therefore$Ratio of first two number=$\frac{6x}{5}:\frac{3x}{2}=12x:15x=4:5$

$\displaystyle \frac{M}{a}=m+n;\frac{N}{b}=m-n$
$\displaystyle \therefore \left ( \frac{M}{a}+\frac{N}{b} \right )\div \left ( \frac{M}{a}-\frac{N}{b} \right )=2m\div 2n=\frac{m}{n}$

We know,

Length = 2m = 200 cm
 Width = 28 cm
$\dfrac{Length}{ Width}$ = $\dfrac{200}{28}$

The three quantities $a,\,b,\,c$ are said to be in continued proportion if $a:b::b:c$
$\Longrightarrow\dfrac{a}{b}=\dfrac{b}{c}$
$\Longrightarrow a\times c=b^2$
$\Longrightarrow b^2=ac$

The $a:b:c=A:B:C$
can be represented by ratio representation is
$ratio=\dfrac{a}{A}=\dfrac{b}{B}=\dfrac{c}{C}$

$\dfrac{2}{9}=\dfrac{x}{18}$
$\Rightarrow\;9x=36$
$\Rightarrow\;x=4$