What is the cost of flooring a rectangular hall?

I. The length and the breadth of the hall are in the ratio $3 : 2$.

II. The length of the hall is $48 ext{ m}$ and the cost of flooring is Rs. $850$ per sq m.

III. The perimeter of the hall is $160 ext{ m}$ and the cost of flooring is Rs. $850$ per sq m.

Which of the following statements is/are sufficient to find the cost of flooring the hall?

Question

What is the cost of flooring a rectangular hall?

I. The length and the breadth of the hall are in the ratio $3 : 2$.

II. The length of the hall is $48 	ext{ m}$ and the cost of flooring is Rs. $850$ per sq m.

III. The perimeter of the hall is $160 	ext{ m}$ and the cost of flooring is Rs. $850$ per sq m.

Which of the following statements is/are sufficient to find the cost of flooring the hall?

Accepted Answer

**Solution:**

1. From statement I, the ratio of length to breadth is given as $3 : 2$.

2. Statement II provides the length as $48 	ext{ m}$ and the cost of flooring as Rs. $850$ per sq m.

3. Using I and II together:
   - Length, $\ell = 48 	ext{ m}$
   - Breadth, $b = \frac{2}{3} 	imes 48 = 32 	ext{ m}$
   - Area $= \ell 	imes b = 48 	imes 32 = 1536 	ext{ sq m}$
   - Total cost $= 1536 	imes 850 = 	ext{Rs. } 1,305,600$

4. Statement III states the perimeter is $160 	ext{ m}$ and cost per sq m is Rs. $850$.

5. Using I and III together:
   - Perimeter $= 2(\ell + b) = 160 \Rightarrow \ell + b = 80$
   - From ratio $\ell : b = 3 : 2$, let $\ell = 3x$ and $b = 2x$
   - So, $3x + 2x = 80 \Rightarrow 5x = 80 \Rightarrow x = 16$
   - Length $\ell = 3 	imes 16 = 48 	ext{ m}$
   - Breadth $b = 2 	imes 16 = 32 	ext{ m}$
   - Area $= 48 	imes 32 = 1536 	ext{ sq m}$
   - Total cost $= 1536 	imes 850 = 	ext{Rs. } 1,305,600$

6. Therefore, any two statements among I, II, and III are sufficient to find the cost of flooring.

**Answer:** Only I and II

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