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The following questions are accompanied by three statements (I), (II), and (III). You have to determine which statements(s) is/are sufficient/necessary to answer the questions. Two trains A and B are travelling towards each other on the same track. The initial distance between them is 91 km. Find the time, when the two trains will collide. I: The speed of train A is 65 km/h and the speed of B is 104 km/h more than that of train A. II: The ratio of speeds of the two trains is 5: 13. III. Faster train can travel 312 km in 3 hr.

The following questions are accompanied by three statements (I), (II), and (III). You have to determine which statements(s) is/are sufficient/necessary to answer the questions. Two trains A and B are travelling towards each other on the same track. The initial distance between them is 91 km. Find the time, when the two trains will collide. I: The speed of train A is 65 km/h and the speed of B is 104 km/h more than that of train A. II: The ratio of speeds of the two trains is 5: 13. III. Faster train can travel 312 km in 3 hr. Correct Answer Only I

Let distance travelled by slow train be x km in time ‘t’, 

From statement I: 

Speed, 65 = distance/time = x/t 

⇒ t = x/65      ----(1) 

for faster train, in same time ‘t’, 

Speed, 169 = distance/time = x/t 

⇒ t = (91 - x)/169      ----(2) 

Equating (1) & (2), 

⇒ x/65 = (91 - x)/169 

⇒ 169x = 5915 – 65x 

⇒ 104x = 5915

⇒ x = 56.875 km 

Putting in (1),

⇒ t = x/65 = (5915/104)/65 = 35/(8 × 5) 

= 35/40 = 0.875 hr = 0.875 × 60 = 52.5 minutes.

∴ only statement I is sufficient to answer the question.

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