Two trains start from Delhi and Patna, and travel towards Patna and Delhi, respectively. After passing each other, they take 4h 48 min and 3 h 20 min to reach Patna and Delhi, respectively. If the train starting from Delhi is moving at a speed of 45 km/h, then find the speed of the other train.

Correct option is C

​Given:

Train from Delhi takes 4h 48 min (4.8 hours) after meeting.

Train from Patna takes 3h 20 min (3.33 hours) after meeting.

Speed of train from Delhi = 45 km/h.

Concept Used:
The time taken by two trains after meeting is inversely proportional to their speeds.

Formula Used:
If $$S_1$$​ and $$S_2$$​ are the speeds, then:

​$$(\frac{S_1}{S_2})^2 = \frac{\text{Time taken by other train}}{\text{Time taken by first train}}$$​​

Solution:
Let the speed of the second train be $$S_2$$​.

​$$(\frac{45}{S_2})^2 = \frac{3.33}{4.8}$$​​

​​​$$2025 \times 480 = S_2^2 \times 333\\ \ \\S_2^2 = \frac{2025 \times 480}{333} = 2919 \,$$​​

​$$S_2 = \sqrt{ 2919} \ = 54 \ km/h$$​​