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

Step 1: Set convenient values.
Let the common distance be 16 km, and the speeds be 1, 4 and 16 kmph respectively (matching the given ratio).

Step 2: Find the time taken by each.
Time \(=\dfrac{\text{distance}}{\text{speed}}\): scooter \(=\dfrac{16}{1}=16\) h, car \(=\dfrac{16}{4}=4\) h, train \(=\dfrac{16}{16}=1\) h.

Step 3: Find (time ÷ velocity) for each.
Scooter: \(\dfrac{16}{1}=16\). Car: \(\dfrac{4}{4}=1\). Train: \(\dfrac{1}{16}\).

Step 4: Express as a ratio.
\(16:1:\dfrac{1}{16}\). Multiplying through by 16 to clear the fraction: \(256:16:1\).

Step 5: Final Answer.
The ratio is 256:16:1, so option A is correct.