Multiple choice

The question is followed by two statements, I and II. Mark the answer as per the given conditions. [CAT 1991] A train started from Station A, developed engine trouble and reached Station B, 40 minutes late. What is the distance between Stations A and B? I. The engine trouble developed after travelling 40 km from Station A and the speed reduced to (1/4)th of the original speed. II. The engine trouble developed after travelling 40 km from station A in two hours and the speed reduced to (1/4)th of the original speed.

  1. statement I alone is required to answer the question, but not statement II.

  2. statement II alone is required to answer the question, but not statement I.

  3. both statements I and II together are needed to answer the question.

  4. can be answered by both statements independently.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement I provides the distance and speed ratio but not the time taken to travel the first 40 km. Statement II specifies the time taken (2 hours) to travel the first 40 km, allowing for the calculation of the original speed and the subsequent delay, which makes it sufficient to find the total distance.

AI explanation

Let the original speed be v and the total distance be D, and from the second statement we know the train travelled 40 km in 2 hours, meaning its initial speed v was 20 km/hr. The engine trouble developed after 40 km, leaving a distance of D minus 40 km to be travelled at the reduced speed of one fourth of 20, which is 5 km/hr. The normal time for the entire journey is D divided by 20, but the actual time taken is 2 hours plus the quantity of D minus 40 divided by 5, and this actual time is 40 minutes more than the normal time. Solving the equation D divided by 20 plus two thirds equals 2 plus the quantity of D minus 40 divided by 5 gives 3D plus 40 equals 60 plus 12D minus 480, leading to 9D equals 540, so the distance is 60 km. Statement II provides the necessary time of 2 hours to find the original speed, making it independently sufficient, whereas Statement I does not provide the original speed value and is insufficient.

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