The cost of carpeting a room is Rs. 120. If the width had been 4 metres less, the cost of the carpet would have been Rs. 20 less. The width of the room is :

Options

A. 24 m
B. 20m
C. 25m
D. 18.5 m

Answer

To solve the problem step by step, we will follow the reasoning outlined in the video transcript.

### Step-by-Step Solution:

1. **Define Variables:**
- Let the length of the room be \( X \) meters.
- Let the width of the room be \( Y \) meters.

2. **Set Up the First Equation:**
- The cost of carpeting the room is given as Rs. 120. The cost of carpeting is proportional to the area of the room.
- Therefore, the area of the room can be expressed as:
\[ X \times Y = 120 \]
- This is our first equation.

3. **Set Up the Second Equation:**
- If the width had been 4 meters less, the new width would be \( Y - 4 \).
- The cost of carpeting would then be Rs. 20 less, which means the new cost would be Rs. 100.
- Thus, we can write the second equation as:
\[ X \times (Y - 4) = 100 \]
- This is our second equation.

4. **Express \( X \) from the First Equation:**
- From the first equation, we can express \( X \) in terms of \( Y \):
\[ X = \frac{120}{Y} \]

5. **Substitute \( X \) into the Second Equation:**
- Substitute \( X \) in the second equation:
\[ \frac{120}{Y} \times (Y - 4) = 100 \]

6. **Simplify the Equation:**
- Multiply both sides by \( Y \) to eliminate the fraction:
\[ 120(Y - 4) = 100Y \]
- Expanding the left side gives:
\[ 120Y - 480 = 100Y \]

7. **Rearrange the Equation:**
- Move all terms involving \( Y \) to one side:
\[ 120Y - 100Y = 480 \]
- Simplifying gives:
\[ 20Y = 480 \]

8. **Solve for \( Y \):**
- Divide both sides by 20:
\[ Y = \frac{480}{20} = 24 \]

9. **Conclusion:**
- The width of the room is \( Y = 24 \) meters.

### Final Answer:
The width of the room is **24 meters**.