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The dimensions of a rectangular box are in the ratio of 1:2:4 and the difference between the costs of covering it with the cloth and a sheet at the rate of Rs 20 and Rs 20.5 per sq m respectively is Rs 126. Find the dimensions of the box.
- a)2 m, 6 m, 9 m
- b)6 m, 12 m, 24 m
- c)1 m, 2 m, 4 m
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
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To solve this problem, we can start by assigning variables to the dimensions of the rectangular box. Let's say the dimensions are x, 2x, and 4x.
Now, let's calculate the area of the box that needs to be covered with cloth and with a sheet.
The area of the box that needs to be covered with cloth is given by:
Area1 = 2(xy + x(2x) + (2x)(4x))
= 2(7x^2)
= 14x^2
The area of the box that needs to be covered with a sheet is given by:
Area2 = 2(x(2x) + (2x)(4x) + 4x(2x))
= 2(20x^2)
= 40x^2
The difference between the costs of covering the box with cloth and with a sheet is Rs 126. We can set up an equation using the area and the cost per square meter:
20(14x^2) - 20.5(40x^2) = 126
Now, let's solve this equation for x.
280x^2 - 820x^2 = 126
-540x^2 = 126
x^2 = -126/540
x^2 = -7/30
Since the value of x^2 is negative, it means that the dimensions of the box cannot be real numbers. Therefore, the correct answer is "None of these" (option D).
This indicates that there is no solution to the problem as presented. It is possible that there may be a mistake in the problem statement or in the given values.
Now, let's calculate the area of the box that needs to be covered with cloth and with a sheet.
The area of the box that needs to be covered with cloth is given by:
Area1 = 2(xy + x(2x) + (2x)(4x))
= 2(7x^2)
= 14x^2
The area of the box that needs to be covered with a sheet is given by:
Area2 = 2(x(2x) + (2x)(4x) + 4x(2x))
= 2(20x^2)
= 40x^2
The difference between the costs of covering the box with cloth and with a sheet is Rs 126. We can set up an equation using the area and the cost per square meter:
20(14x^2) - 20.5(40x^2) = 126
Now, let's solve this equation for x.
280x^2 - 820x^2 = 126
-540x^2 = 126
x^2 = -126/540
x^2 = -7/30
Since the value of x^2 is negative, it means that the dimensions of the box cannot be real numbers. Therefore, the correct answer is "None of these" (option D).
This indicates that there is no solution to the problem as presented. It is possible that there may be a mistake in the problem statement or in the given values.
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