Question

The rate for 1.20 m wide carpet is Rs. 40 per metre. Find the cost of covering a hall that is 45 m long and 32 m wide with this carpet. Also, find the cost of carpeting the same hall if the carpet is 80 cm wide at Rs. 25 per metre.
A. Rs. 57,600 ; Rs. 36,000
B. Rs. 45,000 ; Rs. 45,000
C. Rs. 48,000 ; Rs. 45,000
D. Rs. 36,000 ; Rs. 57,000

Answer 1

Hint: To solve this question, we need to know the concept of the area of the rectangle, which is the product of the length of the rectangle and the width of the rectangle. We can write it as, area of rectangle = length $\times $ width. Then we can multiply the cost per metre and length to get the total cost.

Complete step-by-step answer:

To solve the given question, we have to find the area of a hall which is 45 m long and 32 m wide and also the cost of carpeting the same hall if the carpet is 80 cm wide at Rs. 25 per metre. Let us consider the figure below.

We have to use the formula of the area of the rectangle to solve this. We know that the area of rectangle = length $\times $ width. Therefore, we can write the area of the floor $=45\times 32=1440{{m}^{2}}$…………(i). So, we get that the area of the floor of a hall with dimensions $45\times 32{{m}^{2}}$ is equal to $1440{{m}^{2}}$.
Now, we have been given that the rate of 1.20 m wide carpet is Rs. 40 per metre, and we have been asked to find the cost of covering the hall with this carpet. For the same, we need to find the length of the carpet that is required to cover the hall. For that we will again apply the formula of area of rectangle, that is, area of floor = length $\times $ width. By substituting the value of area of floor from equation (i), we get $1440{{m}^{2}}=$ length $\times 1.2m=\dfrac{1440}{1.2}m=1200m$. Hence the length is $1200m$.
Now, we have been given the rate of flooring of 1.20 m wide carpet is Rs. 40 per metre. So, we can write,
Cost of covering hall = Rs. (length $\times $ 40) = Rs. (1,200 $\times $ 40) = Rs. 48,000 …………(ii)
We have also been given the rate for flooring with 0.80 m wide carpet is Rs. 25 per metre, which is, Cost of covering hall = Rs. (length $\times $ 25). We know that the length of the carpet is, $\dfrac{\text{Area of floor}}{\text{width of carpet}}=\dfrac{1440}{0.80}=1800m$. So, the rate of covering the hall = Rs. (1800 $\times $ 25) = Rs. 45,000.
Hence, we get the cost of covering the hall with 1.2 m and 80 cm carpet as Rs. 48,00 and as Rs. 45,000, respectively. Therefore, option C is the correct answer.

Note: We must be careful that cost is per metre not per sq. meter, so we have to multiply it with the corresponding length and not the area. The possible points where we can make mistakes is while using the width of 80 cm, that is we have to convert cm to m to get the correct answer, that is $80cm=\dfrac{80}{100}m=0.80m$.