Multiple choice

The length of a room is twice its breadth. The cost of carpeting it at Re. 1 per square metre is Rs. 1800 and the cost of whitewashing only the walls at 50 paise per square metre is Rs. 265, excluding the area of doors and windows of area 10 square metres. The height of the room is

  1. 2.5 m

  2. 2.8 m

  3. 3.2 m

  4. 3 m

  5. 4 m
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D Correct answer
Explanation

Let breadth = x, length = 2x. Area = 2x^2. Cost of carpet = 1 * 2x^2 = 1800 -> x^2 = 900 -> x = 30. Breadth = 30, Length = 60. Wall area = 2*(L+B)H = 2(90)*H = 180H. Wall area - 10 = (265 / 0.5) = 530. 180H = 540 -> H = 3.

AI explanation

The carpeting cost of 1800 rupees at 1 rupee per square metre gives a floor area of 1800 square metres, meaning length * breadth = 1800. Since the length is twice the breadth, we have 2 * breadth^2 = 1800, making the breadth 30 metres and the length 60 metres. The cost of whitewashing the four walls at 0.50 rupees per square metre totals 265 rupees, so the actual area of the walls painted is 265 / 0.50 = 530 square metres. Adding the 10 square metres of excluded doors and windows gives a total wall area of 540 square metres; using the formula 2 * (length + breadth) * height = 540, we get 2 * (60 + 30) * height = 540, making the height 3 metres. The height of the room is 3 m.

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