Multiple choice

STATEMENT(1): Two trains can cross a man who is standing stationary at a certain platform. First train takes 50% less time than second train to cross the man while second train takes 18 s. The trains are coming from same direction. The ratio of their speed is 4:5. STATEMENT (2): There are two more trains at a platform of Lucknow junction. First train crosses the platform one third of its length with a speed of 54km/hr in 1 min. It will cross another train of length double than the length of platform which is standing on platform with 3/5 of its speed. Find the ratio of time taken by the trains to cross each other in statement(1) to the time taken by the trains to cross each other in statement(2).

  1. 125 : 126

  2. 125 : 9

  3. 9 : 125

  4. 126 : 125

  5. None of these

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement 1: Train 2 takes 18s to cross man. Train 1 takes 50% less = 9s. Speed ratio 4:5, let v1=4x, v2=5x. Lengths: L1=4x×9=36x, L2=5x×18=90x. Same direction crossing time = (36x+90x)/(5x-4x) = 126x/x = 126s. Statement 2: First train length L, speed 54km/h=15m/s. Crosses L/3 platform in 60s: L+L/3 = 15×60, 4L/3 = 900, L=675m. Second train length = 2×L/3 = 450m. Speed of first = 15m/s, second = (3/5)×15 = 9m/s. Same direction crossing time = (675+450)/(15-9) = 1125/6 = 187.5s. Ratio = 126:187.5 = 126:125. ✓