A car run along the sides of a square groun with the speed of 20 km./hr., 30 km./hr., 40 km./hr. and 60 km./hr. respectively. Accordingly, what is the average speed of car along the sides of ground ?

Options

A. a)30 km/hr
B. b)75 km/hr
C. c)32 km/hr
D. d)35 km/hr

Answer

To find the average speed of the car running along the sides of a square ground at different speeds, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the distances and speeds**:
- The car runs along the four sides of a square. Let the length of each side of the square be \( x \).
- The speeds for each side are:
- First side: 20 km/hr
- Second side: 30 km/hr
- Third side: 40 km/hr
- Fourth side: 60 km/hr

2. **Calculate the total distance**:
- Since there are four sides, the total distance \( D \) is:
\[ D = x + x + x + x = 4x \]

3. **Calculate the time taken for each side**:
- The time taken \( t \) for each side can be calculated using the formula \( t = \frac{d}{s} \) (distance/speed):
- Time for the first side: \( t_1 = \frac{x}{20} \)
- Time for the second side: \( t_2 = \frac{x}{30} \)
- Time for the third side: \( t_3 = \frac{x}{40} \)
- Time for the fourth side: \( t_4 = \frac{x}{60} \)

4. **Calculate the total time**:
- The total time \( T \) is the sum of the times for each side:
\[ T = t_1 + t_2 + t_3 + t_4 = \frac{x}{20} + \frac{x}{30} + \frac{x}{40} + \frac{x}{60} \]

5. **Find the least common multiple (LCM)**:
- To add these fractions, we need to find the LCM of the denominators (20, 30, 40, 60). The LCM is 120.

6. **Convert each fraction to have a common denominator**:
- Convert each time to have the denominator of 120:
- \( t_1 = \frac{x}{20} = \frac{6x}{120} \)
- \( t_2 = \frac{x}{30} = \frac{4x}{120} \)
- \( t_3 = \frac{x}{40} = \frac{3x}{120} \)
- \( t_4 = \frac{x}{60} = \frac{2x}{120} \)

7. **Add the times together**:
- Now, we can add the times:
\[ T = \frac{6x + 4x + 3x + 2x}{120} = \frac{15x}{120} = \frac{x}{8} \]

8. **Calculate the average speed**:
- The average speed \( V_{avg} \) is given by the formula:
\[ V_{avg} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{4x}{\frac{x}{8}} = 4x \times \frac{8}{x} = 32 \text{ km/hr} \]

### Final Answer:
The average speed of the car along the sides of the ground is **32 km/hr**.