CAT 1997 — QA Question 14
Answer the next 3 questions based on the following information.
There are 60 students in a class. These students are divided into three groups A, B and C of 15, 20 and 25 students each. The groups A and C are combined to form group D.
An express train travelling at 80 km/hr overtakes a goods train, twice as long and going at 40 km/hr on a parallel track, in 54 s. How long will the express train take to cross a platform of 400 m long?
Answer & solution
- A
36 s
- B
45 s
27 s
- D
None of these
Effective speed of two trains = (80 – 40) = 40 km/hr. (Since they are moving in the same direction as inferred from the word ‘overtakes’). At this speed in 54 s, they would travel an effective distance of = 0.6 km or 600 m. This effective distance should be
equal to the sum of the lengths of the two trains. So, if length of the express train is L, length of the goods train will be 2L. Hence, our equation will be L + 2L = 600 or L = 200 m. So, the time taken by this train to cross a platform 400 m long will be s.
(Note that we have converted the denominator in metres per second. Hence, the factor of ).