Question

The speeds of a scooter, a car and a train are in the ratio of 1 : 4 : 16. If all of them cover an equal distance, then the ratio of (time taken ÷ velocity) for each of the vehicles is:

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

Hint:

Time/velocity for a fixed distance equals distance/velocity²; take the reciprocal of the squared speed ratio.

Answer 1

The Correct Option is A

Since time = distance/speed for equal distances, and we then need time/speed, the whole quantity for each vehicle works out to distance/speed², making it easy to build the ratio directly from the speed ratio.

1. For a fixed distance $D$, (time ÷ velocity) $= \frac{D/v}{v} = \frac{D}{v^2}$.
2. Since $D$ is the same for all three vehicles, the ratio of (time ÷ velocity) across vehicles is just the ratio of $\frac{1}{v^2}$ values.
3. Speeds are in ratio $1:4:16$, so $v^2$ values are in ratio $1:16:256$.
4. Taking reciprocals for $\frac{1}{v^2}$: $\frac{1}{1} : \frac{1}{16} : \frac{1}{256}$, which, multiplied through by 256, becomes $256 : 16 : 1$.

So the correct answer is option A, 256 : 16 : 1.