Question

The speed of scooter, car and train are in the ratio of 1 : 4 : 16. If all of them cover equal distance then the ratio of time taken/velocity for each of the vehicle is:

• A. 256:16:1
• B. 1:4:16
• C. 1:4:16
• D. 16:1:4

Answer 1

The Correct Option is A

To solve the problem, we need to determine the ratio of time taken for the scooter, car, and train to travel the same distance. We know the speeds of the scooter, car, and train are in the ratio of 1:4:16. Let's denote the speed of the scooter as \( v \), the speed of the car as \( 4v \), and the speed of the train as \( 16v \).

Let the distance covered by each vehicle be \( d \). The time taken by each vehicle to cover this distance can be calculated using the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

For the scooter, the time taken is:

\[ \text{Time}_{\text{scooter}} = \frac{d}{v} \]

For the car, the time taken is:

\[ \text{Time}_{\text{car}} = \frac{d}{4v} \]

For the train, the time taken is:

\[ \text{Time}_{\text{train}} = \frac{d}{16v} \]

To find the ratio of time taken by the scooter, car, and train, we take:

\[ \text{Ratio} = \left( \frac{d}{v} : \frac{d}{4v} : \frac{d}{16v} \right) \]

Since the distance \( d \) is constant, it cancels out, giving:

\[ (1 : \frac{1}{4} : \frac{1}{16}) \]

To simplify this ratio, multiply each term by 16 to eliminate the fractions:

\[ (16 \times 1 : 16 \times \frac{1}{4} : 16 \times \frac{1}{16}) = (16 : 4 : 1) \]

Therefore, the ratio of time taken by the vehicles is:

256:16:1