Question

If the cost of x meters of wires is d rupees, then the cost of y meters of wire at the same rate is
A.$$Rs.\left({\displaystyle \frac{xy}{d}}\right)$$
B.$$Rs.\left(xy\right)$$
C.$$Rs.\left(yd\right)$$
D.$$Rs.\left({\displaystyle \frac{yd}{x}}\right)$$

Answer 1

Hint: We are given with the cost of x meters of wire and we are asked to find the cost of y meters. So we will use the unitary method here. With the help of which we will be able to find the correct answer.

Complete step-by-step answer:
Given that the cost of x meters of wires is d rupees.
The cost of 1meter of such wire is
 $$\begin{gathered} xmeters\to Rs.d \\ 1meter\to ? \\ \Rightarrow ?={\displaystyle \frac{d}{x}} \end{gathered}$$
Now we have to find the cost of y meters of wire at the same rate.
So cost of y meters of wire is $$\Rightarrow y{\displaystyle \frac{d}{x}}$$
This is the cost of y meters of wire $$Rs.{\displaystyle \frac{yd}{x}}$$ .
So the correct option is D.


Note: Students generally make mistakes in these types of problems. They just focus that the cost of x meters is Rs.d then the cost of y meters is Rs.yd , but this is not the correct answer.Let’s elaborate this concept.
Suppose we say that the cost of 1 chocolate is Rs.5 then the cost of 2 chocolates will be? This we can answer very easily that is Rs.10. But if we are given that the cost of 9 flowers is Rs.20 then what is the cost of 3 such flowers? Now something needs to be calculated! This is the time we need a unitary method.
$$\begin{gathered} 9flowers\to Rs.20 \\ 1flowers\to ? \\ \Rightarrow ?={\displaystyle \frac{20}{9}}={\displaystyle \frac{20}{9}} \\ \Rightarrow 3flowers={\displaystyle \frac{20}{9}}\times 3={\displaystyle \frac{20}{3}} \end{gathered}$$
We used the same approach in our problem above. Hope you understood!