Question

Set up a table and solve the following problems. Use unitary method to verify the answer.
The cost of $97$ metre of cloth is $Rs.242.50$. What length of this can be purchased for $Rs.302.50$?

Answer 1

Draw a table and solve the problem

Given: Length of the cloth purchased for $Rs.242.50=97m$

Let Length of the cloth purchased for $Rs.302.50$ be ${}^{\prime }{x}^{\prime }m$

Cloth length $\left(m\right)$	$97$	$x$
Cost $(Rs.)$	$242.50$	$302.50$

Clearly, the larger the length of the cloth, greater will be the cost of the cloth. So, it is a case of direct variation.

Therefore, ratio of length of the cloth to the cost would be same for both the cases.

$\Rightarrow \frac{97}{242.50}=\frac{x}{302.50}$

$\Rightarrow x=302.50\times \frac{97}{242.50}$

$\Rightarrow x=121$

Hence, $121m$ of the cloth can be purchased for $Rs.302.5$.

Verify using unitary method

Given: Length of the cloth purchased for $Rs.242.50=97m$

$\Rightarrow$Length of cloth purchased for $Re.1=\frac{97}{242.50}m$

$\Rightarrow$Length of cloth purchased for $Rs.302.50$

$=\frac{97}{242.50}\times 302.50$

$=121m$

Thus, $121m$ of the cloth can be purchased for $Rs.302.5$.

Hence, verified.