Question

If the cost of \[93m\] of a certain kind of plastic sheet is $Rs.1395$, then what would it cost to buy $105m$ of such a plastic sheet?

Answer 1

Hint:
Using the given cost, we can calculate the unit cost (that is, cost of $1m$ of sheet). Unit cost is found by dividing the cost of a certain length by the length itself. And the cost of the required length is found by multiplying the length by the unit cost.
Useful formula:
If an article costs $Rs.x$ per unit, then the cost of $k$ units is $Rs.kx$.

Complete step by step solution:
Given that the cost of \[93m\] of a certain kind of plastic sheet is $Rs.1395$.
We are asked to find the cost of $105m$ of the sheet.
First, using the cost of $93m$, we can calculate the cost of $1m$.
Cost of $1m$ is obtained by dividing the cost of $93m$ by $93$.
Cost of $1m$, $C = \dfrac{{1395}}{{93}} = 15$
Now we have to find the cost of $105m$ of plastic sheet.
If an article costs $Rs.x$ per unit, then the cost of $k$ units is $Rs.kx$.
Using this result,
Cost of $105m$ of plastic sheet, ${C_{105}} = 105 \times 15 = 1575$

$\therefore $ The answer is $Rs.1575$.

Note:
Alternative method:
The cost of \[105m\] of the plastic sheet can be directly found without finding the unit cost. This can be done by the concept of ratios.
We are given $93m$ cost $Rs.1395$.
Let the cost of $105m$ be $x$. Then we have, $\dfrac{{93}}{{105}} = \dfrac{{1395}}{x}$
This gives value of $x = \dfrac{{1395 \times 105}}{{93}} = 1575$
So we can calculate the required cost in a single step. But we must be careful about the units. Here both the lengths are given in metres. If not so, we have to change it uniformly and then find the cost.