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The cost of white washing one m2 is Rs 50. What will be the maximum amount saved in painting the room in the most economical way, if the sum of the length, breadth and height is 21 m and all the sides are integers (floor is not to be white washed)?
- a)Rs 1,08,050
- b)Rs 8,400
- c)Rs 9,300
- d)Rs 8,540
Correct answer is option 'C'. Can you explain this answer?
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The cost of white washing one m2 is Rs 50. What will be the maximum am...
The amount saved would be maximum only when the difference of maximum area and minimum area to be painted is maximum.
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The cost of white washing one m2 is Rs 50. What will be the maximum am...
Problem Statement:
The cost of white washing one m2 is Rs 50. What will be the maximum amount saved in painting the room in the most economical way, if the sum of the length, breadth and height is 21 m and all the sides are integers (floor is not to be white washed)?
Solution:
Let us assume the dimensions of the room to be x, y and z where x, y, and z are integers.
Given, x + y + z = 21
To minimize the cost of whitewashing, we need to minimize the surface area of the room. The surface area of the room is given by:
2xy + 2xz + 2yz
Substituting z = 21 - x - y, we get:
2xy + 2x(21 - x - y) + 2y(21 - x - y)
Simplifying the above expression, we get:
42x + 42y - 2x^2 - 2y^2 - 2xy
To minimize the above expression, we need to maximize x*y. Since x, y and z are integers, we can use trial and error method to find the maximum value of x*y.
We can use the following table to find the maximum value of x*y.
| x | y | x*y |
|---|---|-----|
| 1 | 10 | 10 |
| 2 | 9 | 18 |
| 3 | 8 | 24 |
| 4 | 7 | 28 |
| 5 | 6 | 30 |
| 6 | 5 | 30 |
| 7 | 4 | 28 |
| 8 | 3 | 24 |
| 9 | 2 | 18 |
| 10 | 1 | 10 |
From the above table, we can see that the maximum value of x*y is 30, which occurs when x=5 and y=6.
Therefore, the dimensions of the room are 5m x 6m x 10m.
The surface area of the room is 2xy + 2xz + 2yz = 220 m^2.
The cost of whitewashing the room is 220*50 = Rs 11,000.
If we paint only the four walls of the room (excluding the floor and ceiling), the surface area to be painted is (5*10 + 6*10)*2 = 220 m^2.
The cost of painting the four walls of the room is 220*50 = Rs 11,000.
Therefore, the maximum amount saved in painting the room in the most economical way is Rs 11,000 - Rs 9,300 = Rs 1,700.
Hence, option C is the correct answer.
The cost of white washing one m2 is Rs 50. What will be the maximum amount saved in painting the room in the most economical way, if the sum of the length, breadth and height is 21 m and all the sides are integers (floor is not to be white washed)?
Solution:
Let us assume the dimensions of the room to be x, y and z where x, y, and z are integers.
Given, x + y + z = 21
To minimize the cost of whitewashing, we need to minimize the surface area of the room. The surface area of the room is given by:
2xy + 2xz + 2yz
Substituting z = 21 - x - y, we get:
2xy + 2x(21 - x - y) + 2y(21 - x - y)
Simplifying the above expression, we get:
42x + 42y - 2x^2 - 2y^2 - 2xy
To minimize the above expression, we need to maximize x*y. Since x, y and z are integers, we can use trial and error method to find the maximum value of x*y.
We can use the following table to find the maximum value of x*y.
| x | y | x*y |
|---|---|-----|
| 1 | 10 | 10 |
| 2 | 9 | 18 |
| 3 | 8 | 24 |
| 4 | 7 | 28 |
| 5 | 6 | 30 |
| 6 | 5 | 30 |
| 7 | 4 | 28 |
| 8 | 3 | 24 |
| 9 | 2 | 18 |
| 10 | 1 | 10 |
From the above table, we can see that the maximum value of x*y is 30, which occurs when x=5 and y=6.
Therefore, the dimensions of the room are 5m x 6m x 10m.
The surface area of the room is 2xy + 2xz + 2yz = 220 m^2.
The cost of whitewashing the room is 220*50 = Rs 11,000.
If we paint only the four walls of the room (excluding the floor and ceiling), the surface area to be painted is (5*10 + 6*10)*2 = 220 m^2.
The cost of painting the four walls of the room is 220*50 = Rs 11,000.
Therefore, the maximum amount saved in painting the room in the most economical way is Rs 11,000 - Rs 9,300 = Rs 1,700.
Hence, option C is the correct answer.
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The cost of white washing one m2 is Rs 50. What will be the maximum amount saved in painting the room in the most economical way, if the sum of the length, breadth and height is 21 m and all the sides are integers (floor is not to be white washed)?a)Rs 1,08,050b)Rs 8,400c)Rs 9,300d)Rs 8,540Correct answer is option 'C'. Can you explain this answer?
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The cost of white washing one m2 is Rs 50. What will be the maximum amount saved in painting the room in the most economical way, if the sum of the length, breadth and height is 21 m and all the sides are integers (floor is not to be white washed)?a)Rs 1,08,050b)Rs 8,400c)Rs 9,300d)Rs 8,540Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The cost of white washing one m2 is Rs 50. What will be the maximum amount saved in painting the room in the most economical way, if the sum of the length, breadth and height is 21 m and all the sides are integers (floor is not to be white washed)?a)Rs 1,08,050b)Rs 8,400c)Rs 9,300d)Rs 8,540Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The cost of white washing one m2 is Rs 50. What will be the maximum amount saved in painting the room in the most economical way, if the sum of the length, breadth and height is 21 m and all the sides are integers (floor is not to be white washed)?a)Rs 1,08,050b)Rs 8,400c)Rs 9,300d)Rs 8,540Correct answer is option 'C'. Can you explain this answer?.
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