Two trains A and B cross each other in 12 seconds when they move towards each other. Speed of train A and train B is 81 km/hr and 54 km/hr respectively. Length of train A is 150 metres more than the length of train B.

Which of the following can be obtained from the above given information?

(i) Time taken by train B to cross a man moving in the same direction as of train B.

(ii) Time taken by train A to cross a platform of half of its length.

(iii) Length of train A.

(iv) Speed of another train C whose length is equal to average of length of train A and B.

Question

Two trains A and B cross each other in 12 seconds when they move towards each other. Speed of train A and train B is 81 km/hr and 54 km/hr respectively. Length of train A is 150 metres more than the length of train B.

Which of the following can be obtained from the above given information?

(i) Time taken by train B to cross a man moving in the same direction as of train B.

(ii) Time taken by train A to cross a platform of half of its length.

(iii) Length of train A.

(iv) Speed of another train C whose length is equal to average of length of train A and B.

Accepted Answer

**Solution:**

1. Let the length of train B be *x* meters.
   Then length of train A = *x + 150* meters.

2. Given:
   - Speed of train A = 81 km/hr = $81 \times \frac{5}{18} = 22.5 \text{ m/s}$
   - Speed of train B = 54 km/hr = $54 \times \frac{5}{18} = 15 \text{ m/s}$

3. When trains move towards each other, their relative speed = $22.5 + 15 = 37.5 \text{ m/s}$

4. They cross each other in 12 seconds, so:
   $$
   \text{Sum of lengths} = \text{Relative speed} \times \text{Time} = 37.5 \times 12 = 450 \text{ meters}
   $$

5. Therefore:
   $$
   x + (x + 150) = 450 \implies 2x + 150 = 450 \implies 2x = 300 \implies x = 150
   $$

6. Length of train A = $150 + 150 = 300 \text{ meters}$
   Length of train B = $150 \text{ meters}$

7. Now, check each part:

- (i) Time taken by train B to cross a man moving in the same direction as train B:
     - Cannot be found because speed of the man is not given.

- (ii) Time taken by train A to cross a platform of half its length:
     - Length of platform = $\frac{300}{2} = 150 \text{ meters}$
     - Speed of train A = 22.5 m/s
     - Time = $\frac{\text{Length of train A} + \text{Length of platform}}{\text{Speed of train A}} = \frac{300 + 150}{22.5} = \frac{450}{22.5} = 20 \text{ seconds}$

- (iii) Length of train A:
     - Already found as 300 meters.

- (iv) Speed of another train C whose length is average of lengths of A and B:
     - Length of train C = $\frac{300 + 150}{2} = 225 \text{ meters}$
     - No information about speed of train C is given, so cannot be found.

**Answer:** (ii) and (iii)

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