Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:

Step 1: Understand the scenario

• Two trains start at the same time from Howrah and Patna towards each other.
• They meet at some point.
• After meeting:
  • Train A (from Howrah) takes 9 hours to reach Patna.
  • Train B (from Patna) takes 16 hours to reach Howrah.

Step 2: Use the concept of inverse time-speed relationship

When two objects move toward each other and meet, the distances left after meeting are inversely proportional to their speeds.

So, Speed of Train A : Speed of Train B = √(1 / 9) : √(1 / 16)
                                   = 1/3 : 1/4
                                   = 4 : 3

Answer: 4 : 3

The ratio of their speeds is 4:3.

This classic problem is solved using the concept that the time taken to complete the remaining journey after meeting is inversely proportional to the speed of the trains. Such problems are commonly asked in aptitude exams to test conceptual clarity on relative speed and ratios.