Question

The length of a room is double its breadth. The cost of coloring the ceiling at Rs.\ 25 per sq.\ meter is Rs.\ 5000 and the cost of painting the four walls at Rs.\ 240 per sq.\ metre is Rs.\ 64800. Find the height of the room :

Answer 1

Correct Answer: 2

Concept:

• Ceiling area = \(l \times b\)
• Area of four walls = \(2h(l+b)\)

Step 1: Find ceiling area.
\[ \frac{5000}{25} = 200 \text{ m}^2 \] \[ l \times b = 200 \] Given \(l = 2b\): \[ 2b^2 = 200 \Rightarrow b^2 = 100 \Rightarrow b = 10,\quad l = 20 \]
Step 2: Find wall area.
\[ \frac{64800}{240} = 270 \text{ m}^2 \] \[ 2h(l+b) = 270 \] \[ 2h(20+10) = 270 \Rightarrow 60h = 270 \Rightarrow h = 4.5 \]
Step 3: Option analysis.

• (A) Incorrect $\times$
• (B) Correct \checkmark
• (C) Incorrect $\times$
• (D) Incorrect $\times$
• (E) Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (B).