Two trains A and B are running in the same direction and cross each other in $32X$ seconds. Find the value of $X$.

Statements:

(I) Train B crosses a 140 meters bridge in 22.4 seconds.

(II) Train A can cross a tree in 19 seconds.

(III) Length of train A is equal to length of train B.

Question

Two trains A and B are running in the same direction and cross each other in $32X$ seconds. Find the value of $X$.

Statements:

(I) Train B crosses a 140 meters bridge in 22.4 seconds.

(II) Train A can cross a tree in 19 seconds.

(III) Length of train A is equal to length of train B.

Accepted Answer

**Solution:**

1. We need to find the value of $X$ in the time taken for trains A and B to cross each other, which is $32X$ seconds.

2. Statement I: Train B crosses a 140 meters bridge in 22.4 seconds.
   - This allows us to find the speed of train B.
   - Speed of train B = $\frac{140}{22.4} = 6.25$ m/s.

3. Statement II: Train A can cross a tree in 19 seconds.
   - Crossing a tree means the train covers its own length in 19 seconds.
   - So, length of train A = speed of train A $	imes$ 19 seconds.

4. Statement III: Length of train A is equal to length of train B.
   - This relation helps connect the lengths of both trains.

5. To find $X$, we need the speeds and lengths of both trains.
   - From Statement I, we get speed of train B.
   - From Statement II, we get length of train A in terms of speed of train A.
   - Statement III equates lengths of A and B, so length of train B = length of train A.

6. Using Statements I and III alone, we cannot find speed of train A, so insufficient.

7. Using Statements II and III, we can express lengths equal and use speed of train A to find length, but speed of train B is unknown.

8. Using Statements I and II alone, lengths are unknown and not related, so insufficient.

9. Using Statements I and III together or II and III together, we can find the required values to calculate $X$.

**Answer:** Either statement I & III or statement II & III together

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