Question

The length of a piece of cloth varies directly as its cost. The cost of cloth having length $24$ $m$ is Rs. $840$. Find the length of a cloth having cost Rs. $525$.

Answer 1

Let $l$ be the length of the cloth and $c$ be its cost.
Then, $l\propto c$
$\therefore l=kc$ (where $k$ is a constant of variation.)
Substituting $l=24$ and $c=840$
$\Rightarrow 24=k\times 840$
$\Rightarrow k=\frac{24}{840}$
$\Rightarrow k=\frac{1}{35}$
Now, taking $c=$ Rs. $525$ and $k=\frac{1}{35}$
$\Rightarrow l=\frac{1}{35}\times 525$
$\Rightarrow l=15$ $m$
Hence, the length of a cloth is $15$ $m$.