Explanation:

Let’s break it down, step by step: 

- Shatabadi Express: 180 m, crosses a tree in 12 sec ? Speed = 180/12 = 15 m/s.

- August Express: 240 m, crosses a tree in 12 sec (because the problem says “same time as Shatabadi”) ? Speed = 240/12 = 20 m/s.

- They both hit the bridge of 270 m at the same time, moving in opposite directions—so when they cross each other, you add their speeds. Relative speed = 15 + 20 = 35 m/s.

- To fully cross one another, each needs to clear the other’s entire length. So, distance = 180 + 240 = 420 meters.

- Time to cross each other = Total distance / Relative speed = 420 / 35 = 12 seconds.

Now, about those increased times:

- “If time taken by Shatabadi to cross a tree is 66.67% more” ? 12 × 1.6667 = 20 seconds ? new speed = 180 / 20 = 9 m/s.

- “Time taken by August to cross a tree is 150% more” ? 12 × 2.5 = 30 seconds ? new speed = 240 / 30 = 8 m/s.

- Relative speed now = 9 + 8 = 17 m/s.

- Time to cross each other with new speeds = 420 / 17 ˜ 24.7 seconds.

Option 1: 24.7 is the correct answer.

- Option 2 (2.80), Option 3 (2.90), Option 4 (3.0), Option 5 (3.2)—these are way off and don’t fit the numbers or math at all.

- The crucial trick: Don't get distracted by the bridge; crossing each other means sum of their lengths divided by sum of their (relative) speeds.

- The upgrade in crossing time means much lower speeds, so the time to cross each other jumps way up—right to option 1.

You nailed it.