The speeds of three cars are in the ratio of 2 : 3 : 5 Find the ratio of the time taken by the above cars to travel the same distance.

Options

A. `15 : 10 : 6`
B. `6 : 10 : 15`
C. `10 : 15 : 6 `
D. `10 : 6 : 15 `

Answer

To find the ratio of the time taken by three cars to travel the same distance, given their speeds in the ratio of 2:3:5, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Speeds**:
Let the speeds of the three cars A, B, and C be represented as:
- Speed of Car A = 2x
- Speed of Car B = 3x
- Speed of Car C = 5x
Here, x is a common multiplier.

2. **Understand the Relationship**:
The relationship between speed, time, and distance is given by the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Since the distance traveled by all cars is the same, we can express time in terms of speed:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

3. **Set the Distance**:
Let the distance traveled by each car be D. Then the time taken by each car can be expressed as:
- Time taken by Car A = \(\frac{D}{2x}\)
- Time taken by Car B = \(\frac{D}{3x}\)
- Time taken by Car C = \(\frac{D}{5x}\)

4. **Calculate the Time Ratios**:
To find the ratio of the times taken by the cars, we can write:
- Time ratio = \(\frac{D}{2x} : \frac{D}{3x} : \frac{D}{5x}\)

Since D and x are common in all terms, we can simplify this to:
\[ \text{Time ratio} = \frac{1}{2} : \frac{1}{3} : \frac{1}{5} \]

5. **Finding a Common Denominator**:
The least common multiple (LCM) of the denominators (2, 3, 5) is 30. We can express each term with a denominator of 30:
- \(\frac{1}{2} = \frac{15}{30}\)
- \(\frac{1}{3} = \frac{10}{30}\)
- \(\frac{1}{5} = \frac{6}{30}\)

6. **Final Time Ratio**:
Therefore, the time ratio becomes:
\[ \text{Time ratio} = 15 : 10 : 6 \]

### Conclusion:
The ratio of the time taken by the three cars to travel the same distance is **15 : 10 : 6**.