CAT 1997 — QA Question 14

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 $\frac{(40\times 54)}{3600}$ = 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 $\frac{(200+400)}{\left(80\times {\displaystyle \frac{5}{18}}\right)}=27$ s.

(Note that we have converted the denominator in metres per second. Hence, the factor of $\frac{5}{18}$).