Tag: direct proportion

The distance travelled is directly proportional to the number of hours travelled.

So, if  in $ 4 $ hours, $ 120\ km $ is travelled then in $ 1 $ hour  distance travelled is $  \dfrac{ 120 }{4}\ km $  

And in  $ 6 $ hours, distance travelled is  $ 6 \times \dfrac{ 120 }{4}  = 180\ km $

By definition of proportionality,

Let capacity of drum  $=  x$ litres
Initially, drum was $\dfrac {3x}{4}$ part filled
$30$ litres oil drawn then it become, $\dfrac {7x}{12}$ part.
Now, according to question,
$\dfrac {3x}{4} - \dfrac {7x}{12} = 30$
$\Rightarrow \dfrac {(9x - 7x)}{12} = 30$
$\Rightarrow 2x = 360$
$\Rightarrow x = 180$ litres

Cost of cloth is directly proportional to its length.
$10 = 2\times k \Rightarrow k = 5$    , where k is the cost of cloth per meter
$\therefore$ Cost of $100\ m$ cloth $=5\times 100 = 500$.

$\dfrac{x}{y}=K$ (Direct proportion)

$a$ and $b$ are in direct proportion
$\therefore \dfrac {a}{b} = k = \dfrac {2}{14} = \dfrac {3}{21} = \dfrac {1}{7}$
$\therefore \dfrac {4}{x} = \dfrac {1}{7} \Rightarrow x = 28$.

$\dfrac {a}{b} = \dfrac {3}{9} = \dfrac {7}{21} = \dfrac {10}{30} = \dfrac {11}{33} = \dfrac {1}{3} = k$
$\therefore a$ and $b$ are in direct proportion.

$a\propto \dfrac {1}{b} \Rightarrow a = \dfrac {k _{1}}{b}; k _{1}$ is a constant
$b\propto \dfrac {1}{c} \Rightarrow b = \dfrac {K _{2}}{c}; k _{2}$ is a constant
$\Rightarrow a = \dfrac {k _{1}c}{k _{2}} = k _{3}c; k _{3} = \dfrac {k _{1}}{k _{2}}$ is another constant
$\Rightarrow a\propto c$