Question : The ratio of speed of the three racers is 5 : 2 : 1. What is the respective ratio of time taken by the three racers to cover the same distance?
Option 1: 2 : 5 : 10
Option 2: 2 : 5 : 8
Option 3: 5 : 2 : 10
Option 4: 2 : 5 : 3
Correct Answer: 2 : 5 : 10
Solution :
Given: The ratio of the speed of the three racers is 5 : 2 : 1.
Let $y$ km be the distance to be travelled, and the three racers' speeds are $5x,2x,$ and $x$.
We know the formula, Time = $\frac{\text{Distance}}{\text{Speed}}$
Time taken by the first racer= $\frac{y}{5x}$
Time taken by the second racer = $\frac{y}{2x}$
Time taken by the third racer = $\frac{y}{x}$
The respective ratio of time taken by the three racers to cover the same distance
= $\frac{y}{5x}: \frac{y}{2x}: \frac{y}{x}=2:5:10$
Hence, the correct answer is 2 : 5 : 10.
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