Question

Two trains meet. After meeting reach in 4h and 9h. Find speed ratio.

• A. 2:1
• B. 3:2
• C. 4:3
• D. 5:4

Hint:

Memorize this specific formula for "after meeting" train problems. It's a common shortcut that saves significant time compared to setting up complex simultaneous equations. Ensure you correctly identify $t_1$ and $t_2$ (time taken by *first* train after meeting, and time taken by *second* train after meeting, respectively).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The problem describes two trains traveling towards each other, meeting at a point, and then continuing to their respective destinations. The times taken by each train *after* meeting to reach the other train's starting point are given. We need to find the ratio of their speeds.

Step 2: Key Formula or Approach:
For two objects starting at points A and B, traveling towards each other, meeting at point M, and then continuing their journeys such that they reach the opposite starting points in times $t_1$ and $t_2$ respectively (time *after* meeting), the ratio of their speeds ($v_A$ and $v_B$) is given by the formula:
\[ \frac{v_A}{v_B} = \sqrt{\frac{t_2}{t_1}} \]

Step 3: Detailed Explanation:
Let $v_A$ be the speed of the first train and $v_B$ be the speed of the second train.
Let $t_1$ be the time taken by the first train *after* meeting to reach the other's starting point = 4 hours.
Let $t_2$ be the time taken by the second train *after* meeting to reach the other's starting point = 9 hours.
Applying the formula:
\[ \frac{v_A}{v_B} = \sqrt{\frac{9}{4}} \]
\[ \frac{v_A}{v_B} = \frac{3}{2} \]
So the speed ratio is 3:2.

Step 4: Final Answer:
The speed ratio is 3:2.