The perimeters of front wheel and black wheel of a two wheeler are 6ft and 9ft respectively. The front wheel takes 10 revolutions more than back wheel in travelling a distance x. The value of x is

Options

A. 360ft
B. 144ft
C. 540ft
D. 180ft

Answer

To solve the problem, we need to find the distance \( x \) that the two-wheeler travels, given the perimeters of the front and back wheels and the relationship between the number of revolutions they make.

### Step-by-step Solution:

1. **Identify the given information:**
- Perimeter of the front wheel = 6 ft
- Perimeter of the back wheel = 9 ft
- The front wheel takes 10 more revolutions than the back wheel.

2. **Let the number of revolutions of the back wheel be \( y \).**
- Therefore, the number of revolutions of the front wheel = \( y + 10 \).

3. **Calculate the distance traveled by each wheel:**
- Distance traveled by the back wheel = Perimeter × Number of revolutions = \( 9y \) ft.
- Distance traveled by the front wheel = Perimeter × Number of revolutions = \( 6(y + 10) \) ft.

4. **Set the distances equal to each other:**
- Since both wheels travel the same distance \( x \), we can set up the equation:
\[ 9y = 6(y + 10) \]

5. **Expand and simplify the equation:**
- Expanding the right side:
\[ 9y = 6y + 60 \]
- Now, subtract \( 6y \) from both sides:
\[ 9y - 6y = 60 \]
- This simplifies to:
\[ 3y = 60 \]

6. **Solve for \( y \):**
- Divide both sides by 3:
\[ y = 20 \]

7. **Calculate the distance \( x \):**
- Now, substitute \( y \) back into the distance formula for either wheel. Using the back wheel:
\[ x = 9y = 9 \times 20 = 180 \text{ ft} \]

### Final Answer:
The value of \( x \) is 180 feet.