Question

The speeds of 3 cars in the ratio 5 : 4 : 6. The ratio between the time taken by them to travel same distance shall be:

• A. 15:12:11
• B. 12:10:13
• C. 10:20:30
• D. 5:4:6
• E. 12:15:10

Hint:

For equal distances, time ratio is the inverse of speed ratio. Multiply each inverse by the LCM to get integer ratios.

Answer 1

Answer: (E)

Step 1: Understanding the Relationship:
For a fixed distance, time is inversely proportional to speed.
\[ \text{Time} \propto \frac{1}{\text{Speed}} \]

Step 2: Given Speed Ratio:
Let the speeds be \(5k\), \(4k\), and \(6k\).

Step 3: Finding Time Ratio:
Time taken by car 1: \(T_1 = \frac{d}{5k}\)
Time taken by car 2: \(T_2 = \frac{d}{4k}\)
Time taken by car 3: \(T_3 = \frac{d}{6k}\)
Ratio \(T_1 : T_2 : T_3 = \frac{1}{5} : \frac{1}{4} : \frac{1}{6}\)

Step 4: Simplifying the Ratio:
LCM of denominators 5, 4, and 6 is 60.
\[ \frac{1}{5} : \frac{1}{4} : \frac{1}{6} = \frac{60}{5} : \frac{60}{4} : \frac{60}{6} = 12 : 15 : 10 \]